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Dann gilt für die Lösungen:",[1142,1143,1144,1280,1435],"ul",{},[1145,1146,1147,1148,1279],"li",{},"Alle haben denselben Betrag ",[569,1149,1151,1170],{"className":1150},[572],[569,1152,1154],{"className":1153},[576],[578,1155,1156],{"xmlns":580},[582,1157,1158,1167],{},[585,1159,1160],{},[1161,1162,1163,1165],"mroot",{},[591,1164,1048],{},[591,1166,738],{},[606,1168,1169],{"encoding":608},"\\sqrt[n]{r}",[569,1171,1173],{"className":1172,"ariaHidden":614},[613],[569,1174,1176,1180],{"className":1175},[618],[569,1177],{"className":1178,"style":1179},[622],"height:1.04em;vertical-align:-0.2397em;",[569,1181,1184,1215],{"className":1182},[627,1183],"sqrt",[569,1185,1188],{"className":1186},[1187],"root",[569,1189,1191],{"className":1190},[639],[569,1192,1194],{"className":1193},[643],[569,1195,1198],{"className":1196,"style":1197},[647],"height:0.5516em;",[569,1199,1201,1205],{"style":1200},"top:-2.8363em;",[569,1202],{"className":1203,"style":1204},[654],"height:2.5em;",[569,1206,1209],{"className":1207},[659,660,1208,662],"size1",[569,1210,1212],{"className":1211},[627,662],[569,1213,738],{"className":1214},[627,631,662],[569,1216,1219,1270],{"className":1217},[639,1218],"vlist-t2",[569,1220,1222,1265],{"className":1221},[643],[569,1223,1226,1242],{"className":1224,"style":1225},[647],"height:0.8003em;",[569,1227,1231,1235],{"className":1228,"style":1230},[1229],"svg-align","top:-3em;",[569,1232],{"className":1233,"style":1234},[654],"height:3em;",[569,1236,1239],{"className":1237,"style":1238},[627],"padding-left:0.833em;",[569,1240,1048],{"className":1241,"style":1100},[627,631],[569,1243,1245,1248],{"style":1244},"top:-2.7603em;",[569,1246],{"className":1247,"style":1234},[654],[569,1249,1253],{"className":1250,"style":1252},[1251],"hide-tail","min-width:0.853em;height:1.08em;",[1254,1255,1261],"svg",{"xmlns":1256,"width":1257,"height":1258,"viewBox":1259,"preserveAspectRatio":1260},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[1262,1263],"path",{"d":1264},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[569,1266,1269],{"className":1267},[1268],"vlist-s","​",[569,1271,1273],{"className":1272},[643],[569,1274,1277],{"className":1275,"style":1276},[647],"height:0.2397em;",[569,1278],{}," (reelle, positive Wurzel). Sie liegen also auf einem Kreis um den Ursprung.",[1145,1281,1282,1283,1402,1403,997],{},"Ihre Winkel unterscheiden sich jeweils um ",[569,1284,1286,1310],{"className":1285},[572],[569,1287,1289],{"className":1288},[576],[578,1290,1291],{"xmlns":580},[582,1292,1293,1307],{},[585,1294,1295],{},[1296,1297,1298,1305],"mfrac",{},[585,1299,1300,1302],{},[595,1301,703],{},[591,1303,1304],{},"π",[591,1306,738],{},[606,1308,1309],{"encoding":608},"\\frac{2\\pi}{n}",[569,1311,1313],{"className":1312,"ariaHidden":614},[613],[569,1314,1316,1320],{"className":1315},[618],[569,1317],{"className":1318,"style":1319},[622],"height:1.1901em;vertical-align:-0.345em;",[569,1321,1323,1328,1398],{"className":1322},[627],[569,1324],{"className":1325},[1326,1327],"mopen","nulldelimiter",[569,1329,1331],{"className":1330},[1296],[569,1332,1334,1389],{"className":1333},[639,1218],[569,1335,1337,1386],{"className":1336},[643],[569,1338,1341,1356,1367],{"className":1339,"style":1340},[647],"height:0.8451em;",[569,1342,1344,1347],{"style":1343},"top:-2.655em;",[569,1345],{"className":1346,"style":1234},[654],[569,1348,1350],{"className":1349},[659,660,661,662],[569,1351,1353],{"className":1352},[627,662],[569,1354,738],{"className":1355},[627,631,662],[569,1357,1359,1362],{"style":1358},"top:-3.23em;",[569,1360],{"className":1361,"style":1234},[654],[569,1363],{"className":1364,"style":1366},[1365],"frac-line","border-bottom-width:0.04em;",[569,1368,1370,1373],{"style":1369},"top:-3.394em;",[569,1371],{"className":1372,"style":1234},[654],[569,1374,1376],{"className":1375},[659,660,661,662],[569,1377,1379,1382],{"className":1378},[627,662],[569,1380,703],{"className":1381},[627,662],[569,1383,1304],{"className":1384,"style":1385},[627,631,662],"margin-right:0.0359em;",[569,1387,1269],{"className":1388},[1268],[569,1390,1392],{"className":1391},[643],[569,1393,1396],{"className":1394,"style":1395},[647],"height:0.345em;",[569,1397],{},[569,1399],{"className":1400},[1401,1327],"mclose",". Die Lösungen bilden die Ecken eines ",[905,1404,1405,1406,1434],{},"regelmäßigen ",[569,1407,1409,1422],{"className":1408},[572],[569,1410,1412],{"className":1411},[576],[578,1413,1414],{"xmlns":580},[582,1415,1416,1420],{},[585,1417,1418],{},[591,1419,738],{},[606,1421,738],{"encoding":608},[569,1423,1425],{"className":1424,"ariaHidden":614},[613],[569,1426,1428,1431],{"className":1427},[618],[569,1429],{"className":1430,"style":802},[622],[569,1432,738],{"className":1433},[627,631],"-Ecks",[1145,1436,1437,1438,1492,1493,1568,1569,1597],{},"Für ",[569,1439,1441,1460],{"className":1440},[572],[569,1442,1444],{"className":1443},[576],[578,1445,1446],{"xmlns":580},[582,1447,1448,1457],{},[585,1449,1450,1453,1455],{},[591,1451,1452],{},"k",[599,1454,601],{},[591,1456,738],{},[606,1458,1459],{"encoding":608},"k = n",[569,1461,1463,1483],{"className":1462,"ariaHidden":614},[613],[569,1464,1466,1470,1474,1477,1480],{"className":1465},[618],[569,1467],{"className":1468,"style":1469},[622],"height:0.6944em;",[569,1471,1452],{"className":1472,"style":1473},[627,631],"margin-right:0.0315em;",[569,1475],{"className":1476,"style":670},[669],[569,1478,601],{"className":1479},[674],[569,1481],{"className":1482,"style":670},[669],[569,1484,1486,1489],{"className":1485},[618],[569,1487],{"className":1488,"style":802},[622],[569,1490,738],{"className":1491},[627,631]," erhält man wieder ",[569,1494,1496,1515],{"className":1495},[572],[569,1497,1499],{"className":1498},[576],[578,1500,1501],{"xmlns":580},[582,1502,1503,1512],{},[585,1504,1505],{},[1506,1507,1508,1510],"msub",{},[591,1509,735],{},[595,1511,828],{},[606,1513,1514],{"encoding":608},"z_0",[569,1516,1518],{"className":1517,"ariaHidden":614},[613],[569,1519,1521,1525],{"className":1520},[618],[569,1522],{"className":1523,"style":1524},[622],"height:0.5806em;vertical-align:-0.15em;",[569,1526,1528,1531],{"className":1527},[627],[569,1529,735],{"className":1530,"style":763},[627,631],[569,1532,1534],{"className":1533},[635],[569,1535,1537,1559],{"className":1536},[639,1218],[569,1538,1540,1556],{"className":1539},[643],[569,1541,1544],{"className":1542,"style":1543},[647],"height:0.3011em;",[569,1545,1547,1550],{"style":1546},"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;",[569,1548],{"className":1549,"style":655},[654],[569,1551,1553],{"className":1552},[659,660,661,662],[569,1554,828],{"className":1555},[627,662],[569,1557,1269],{"className":1558},[1268],[569,1560,1562],{"className":1561},[643],[569,1563,1566],{"className":1564,"style":1565},[647],"height:0.15em;",[569,1567],{},"; mehr als ",[569,1570,1572,1585],{"className":1571},[572],[569,1573,1575],{"className":1574},[576],[578,1576,1577],{"xmlns":580},[582,1578,1579,1583],{},[585,1580,1581],{},[591,1582,738],{},[606,1584,738],{"encoding":608},[569,1586,1588],{"className":1587,"ariaHidden":614},[613],[569,1589,1591,1594],{"className":1590},[618],[569,1592],{"className":1593,"style":802},[622],[569,1595,738],{"className":1596},[627,631]," verschiedene Lösungen gibt es nicht.",[565,1599,1437,1600,1652,1653,1655,1656,997],{},[569,1601,1603,1622],{"className":1602},[572],[569,1604,1606],{"className":1605},[576],[578,1607,1608],{"xmlns":580},[582,1609,1610,1619],{},[585,1611,1612,1614,1616],{},[591,1613,743],{},[599,1615,601],{},[595,1617,1618],{},"1",[606,1620,1621],{"encoding":608},"w = 1",[569,1623,1625,1643],{"className":1624,"ariaHidden":614},[613],[569,1626,1628,1631,1634,1637,1640],{"className":1627},[618],[569,1629],{"className":1630,"style":802},[622],[569,1632,743],{"className":1633,"style":806},[627,631],[569,1635],{"className":1636,"style":670},[669],[569,1638,601],{"className":1639},[674],[569,1641],{"className":1642,"style":670},[669],[569,1644,1646,1649],{"className":1645},[618],[569,1647],{"className":1648,"style":684},[622],[569,1650,1618],{"className":1651},[627]," heißen die Lösungen ",[905,1654,553],{},": ",[569,1657,1659,1698],{"className":1658},[572],[569,1660,1662],{"className":1661},[576],[578,1663,1664],{"xmlns":580},[582,1665,1666,1695],{},[585,1667,1668,1674,1676],{},[1506,1669,1670,1672],{},[591,1671,735],{},[591,1673,1452],{},[599,1675,601],{},[588,1677,1678,1680],{},[591,1679,1057],{},[585,1681,1682,1684,1686,1688,1690,1693],{},[595,1683,703],{},[591,1685,1452],{},[591,1687,1304],{},[591,1689,1062],{},[591,1691,1692],{"mathvariant":824},"\u002F",[591,1694,738],{},[606,1696,1697],{"encoding":608},"z_k = e^{2k\\pi i\u002Fn}",[569,1699,1701,1757],{"className":1700,"ariaHidden":614},[613],[569,1702,1704,1707,1748,1751,1754],{"className":1703},[618],[569,1705],{"className":1706,"style":1524},[622],[569,1708,1710,1713],{"className":1709},[627],[569,1711,735],{"className":1712,"style":763},[627,631],[569,1714,1716],{"className":1715},[635],[569,1717,1719,1740],{"className":1718},[639,1218],[569,1720,1722,1737],{"className":1721},[643],[569,1723,1726],{"className":1724,"style":1725},[647],"height:0.3361em;",[569,1727,1728,1731],{"style":1546},[569,1729],{"className":1730,"style":655},[654],[569,1732,1734],{"className":1733},[659,660,661,662],[569,1735,1452],{"className":1736,"style":1473},[627,631,662],[569,1738,1269],{"className":1739},[1268],[569,1741,1743],{"className":1742},[643],[569,1744,1746],{"className":1745,"style":1565},[647],[569,1747],{},[569,1749],{"className":1750,"style":670},[669],[569,1752,601],{"className":1753},[674],[569,1755],{"className":1756,"style":670},[669],[569,1758,1760,1764],{"className":1759},[618],[569,1761],{"className":1762,"style":1763},[622],"height:0.888em;",[569,1765,1767,1770],{"className":1766},[627],[569,1768,1057],{"className":1769},[627,631],[569,1771,1773],{"className":1772},[635],[569,1774,1776],{"className":1775},[639],[569,1777,1779],{"className":1778},[643],[569,1780,1782],{"className":1781,"style":1763},[647],[569,1783,1784,1787],{"style":650},[569,1785],{"className":1786,"style":655},[654],[569,1788,1790],{"className":1789},[659,660,661,662],[569,1791,1793,1796,1799,1802,1805,1808],{"className":1792},[627,662],[569,1794,703],{"className":1795},[627,662],[569,1797,1452],{"className":1798,"style":1473},[627,631,662],[569,1800,1304],{"className":1801,"style":1385},[627,631,662],[569,1803,1062],{"className":1804},[627,631,662],[569,1806,1692],{"className":1807},[627,662],[569,1809,738],{"className":1810},[627,631,662],[565,1812,1813,1814,1917,1918,1946,1947,2016],{},"Das Zeichen ",[569,1815,1817,1835],{"className":1816},[572],[569,1818,1820],{"className":1819},[576],[578,1821,1822],{"xmlns":580},[582,1823,1824,1832],{},[585,1825,1826],{},[1161,1827,1828,1830],{},[591,1829,743],{},[591,1831,738],{},[606,1833,1834],{"encoding":608},"\\sqrt[n]{w}",[569,1836,1838],{"className":1837,"ariaHidden":614},[613],[569,1839,1841,1844],{"className":1840},[618],[569,1842],{"className":1843,"style":1179},[622],[569,1845,1847,1873],{"className":1846},[627,1183],[569,1848,1850],{"className":1849},[1187],[569,1851,1853],{"className":1852},[639],[569,1854,1856],{"className":1855},[643],[569,1857,1859],{"className":1858,"style":1197},[647],[569,1860,1861,1864],{"style":1200},[569,1862],{"className":1863,"style":1204},[654],[569,1865,1867],{"className":1866},[659,660,1208,662],[569,1868,1870],{"className":1869},[627,662],[569,1871,738],{"className":1872},[627,631,662],[569,1874,1876,1909],{"className":1875},[639,1218],[569,1877,1879,1906],{"className":1878},[643],[569,1880,1882,1894],{"className":1881,"style":1225},[647],[569,1883,1885,1888],{"className":1884,"style":1230},[1229],[569,1886],{"className":1887,"style":1234},[654],[569,1889,1891],{"className":1890,"style":1238},[627],[569,1892,743],{"className":1893,"style":806},[627,631],[569,1895,1896,1899],{"style":1244},[569,1897],{"className":1898,"style":1234},[654],[569,1900,1902],{"className":1901,"style":1252},[1251],[1254,1903,1904],{"xmlns":1256,"width":1257,"height":1258,"viewBox":1259,"preserveAspectRatio":1260},[1262,1905],{"d":1264},[569,1907,1269],{"className":1908},[1268],[569,1910,1912],{"className":1911},[643],[569,1913,1915],{"className":1914,"style":1276},[647],[569,1916],{}," ist für komplexe ",[569,1919,1921,1934],{"className":1920},[572],[569,1922,1924],{"className":1923},[576],[578,1925,1926],{"xmlns":580},[582,1927,1928,1932],{},[585,1929,1930],{},[591,1931,743],{},[606,1933,743],{"encoding":608},[569,1935,1937],{"className":1936,"ariaHidden":614},[613],[569,1938,1940,1943],{"className":1939},[618],[569,1941],{"className":1942,"style":802},[622],[569,1944,743],{"className":1945,"style":806},[627,631]," nicht eindeutig. Meist bezeichnet es die Lösung ",[569,1948,1950,1967],{"className":1949},[572],[569,1951,1953],{"className":1952},[576],[578,1954,1955],{"xmlns":580},[582,1956,1957,1965],{},[585,1958,1959],{},[1506,1960,1961,1963],{},[591,1962,735],{},[595,1964,828],{},[606,1966,1514],{"encoding":608},[569,1968,1970],{"className":1969,"ariaHidden":614},[613],[569,1971,1973,1976],{"className":1972},[618],[569,1974],{"className":1975,"style":1524},[622],[569,1977,1979,1982],{"className":1978},[627],[569,1980,735],{"className":1981,"style":763},[627,631],[569,1983,1985],{"className":1984},[635],[569,1986,1988,2008],{"className":1987},[639,1218],[569,1989,1991,2005],{"className":1990},[643],[569,1992,1994],{"className":1993,"style":1543},[647],[569,1995,1996,1999],{"style":1546},[569,1997],{"className":1998,"style":655},[654],[569,2000,2002],{"className":2001},[659,660,661,662],[569,2003,828],{"className":2004},[627,662],[569,2006,1269],{"className":2007},[1268],[569,2009,2011],{"className":2010},[643],[569,2012,2014],{"className":2013,"style":1565},[647],[569,2015],{}," mit dem Hauptwert des Arguments.",[560,2018,2020],{"id":2019},"herleitung","Herleitung",[565,2022,2023,2024,2128,2129,2288,2289,2368,2369,2494,2495,2529,2530,2622,2623,997],{},"Man setzt ",[569,2025,2027,2059],{"className":2026},[572],[569,2028,2030],{"className":2029},[576],[578,2031,2032],{"xmlns":580},[582,2033,2034,2056],{},[585,2035,2036,2038,2040,2043,2045],{},[591,2037,735],{},[599,2039,601],{},[591,2041,2042],{},"s",[1050,2044,1052],{},[588,2046,2047,2049],{},[591,2048,1057],{},[585,2050,2051,2053],{},[591,2052,1062],{},[591,2054,2055],{},"ψ",[606,2057,2058],{"encoding":608},"z = s\\,e^{i\\psi}",[569,2060,2062,2080],{"className":2061,"ariaHidden":614},[613],[569,2063,2065,2068,2071,2074,2077],{"className":2064},[618],[569,2066],{"className":2067,"style":802},[622],[569,2069,735],{"className":2070,"style":763},[627,631],[569,2072],{"className":2073,"style":670},[669],[569,2075,601],{"className":2076},[674],[569,2078],{"className":2079,"style":670},[669],[569,2081,2083,2087,2090,2093],{"className":2082},[618],[569,2084],{"className":2085,"style":2086},[622],"height:0.8491em;",[569,2088,2042],{"className":2089},[627,631],[569,2091],{"className":2092,"style":1104},[669],[569,2094,2096,2099],{"className":2095},[627],[569,2097,1057],{"className":2098},[627,631],[569,2100,2102],{"className":2101},[635],[569,2103,2105],{"className":2104},[639],[569,2106,2108],{"className":2107},[643],[569,2109,2111],{"className":2110,"style":2086},[647],[569,2112,2113,2116],{"style":650},[569,2114],{"className":2115,"style":655},[654],[569,2117,2119],{"className":2118},[659,660,661,662],[569,2120,2122,2125],{"className":2121},[627,662],[569,2123,1062],{"className":2124},[627,631,662],[569,2126,2055],{"className":2127,"style":1385},[627,631,662]," an. Nach der Formel von Moivre ist ",[569,2130,2132,2170],{"className":2131},[572],[569,2133,2135],{"className":2134},[576],[578,2136,2137],{"xmlns":580},[582,2138,2139,2167],{},[585,2140,2141,2147,2149,2155],{},[588,2142,2143,2145],{},[591,2144,735],{},[591,2146,738],{},[599,2148,601],{},[588,2150,2151,2153],{},[591,2152,2042],{},[591,2154,738],{},[588,2156,2157,2159],{},[591,2158,1057],{},[585,2160,2161,2163,2165],{},[591,2162,1062],{},[591,2164,738],{},[591,2166,2055],{},[606,2168,2169],{"encoding":608},"z^n = s^n e^{in\\psi}",[569,2171,2173,2217],{"className":2172,"ariaHidden":614},[613],[569,2174,2176,2179,2208,2211,2214],{"className":2175},[618],[569,2177],{"className":2178,"style":756},[622],[569,2180,2182,2185],{"className":2181},[627],[569,2183,735],{"className":2184,"style":763},[627,631],[569,2186,2188],{"className":2187},[635],[569,2189,2191],{"className":2190},[639],[569,2192,2194],{"className":2193},[643],[569,2195,2197],{"className":2196,"style":756},[647],[569,2198,2199,2202],{"style":650},[569,2200],{"className":2201,"style":655},[654],[569,2203,2205],{"className":2204},[659,660,661,662],[569,2206,738],{"className":2207},[627,631,662],[569,2209],{"className":2210,"style":670},[669],[569,2212,601],{"className":2213},[674],[569,2215],{"className":2216,"style":670},[669],[569,2218,2220,2223,2252],{"className":2219},[618],[569,2221],{"className":2222,"style":2086},[622],[569,2224,2226,2229],{"className":2225},[627],[569,2227,2042],{"className":2228},[627,631],[569,2230,2232],{"className":2231},[635],[569,2233,2235],{"className":2234},[639],[569,2236,2238],{"className":2237},[643],[569,2239,2241],{"className":2240,"style":756},[647],[569,2242,2243,2246],{"style":650},[569,2244],{"className":2245,"style":655},[654],[569,2247,2249],{"className":2248},[659,660,661,662],[569,2250,738],{"className":2251},[627,631,662],[569,2253,2255,2258],{"className":2254},[627],[569,2256,1057],{"className":2257},[627,631],[569,2259,2261],{"className":2260},[635],[569,2262,2264],{"className":2263},[639],[569,2265,2267],{"className":2266},[643],[569,2268,2270],{"className":2269,"style":2086},[647],[569,2271,2272,2275],{"style":650},[569,2273],{"className":2274,"style":655},[654],[569,2276,2278],{"className":2277},[659,660,661,662],[569,2279,2281,2285],{"className":2280},[627,662],[569,2282,2284],{"className":2283},[627,631,662],"in",[569,2286,2055],{"className":2287,"style":1385},[627,631,662],". Das soll gleich ",[569,2290,2292,2318],{"className":2291},[572],[569,2293,2295],{"className":2294},[576],[578,2296,2297],{"xmlns":580},[582,2298,2299,2315],{},[585,2300,2301,2303,2305],{},[591,2302,1048],{},[1050,2304,1052],{},[588,2306,2307,2309],{},[591,2308,1057],{},[585,2310,2311,2313],{},[591,2312,1062],{},[591,2314,1065],{},[606,2316,2317],{"encoding":608},"r\\,e^{i\\varphi}",[569,2319,2321],{"className":2320,"ariaHidden":614},[613],[569,2322,2324,2327,2330,2333],{"className":2323},[618],[569,2325],{"className":2326,"style":1096},[622],[569,2328,1048],{"className":2329,"style":1100},[627,631],[569,2331],{"className":2332,"style":1104},[669],[569,2334,2336,2339],{"className":2335},[627],[569,2337,1057],{"className":2338},[627,631],[569,2340,2342],{"className":2341},[635],[569,2343,2345],{"className":2344},[639],[569,2346,2348],{"className":2347},[643],[569,2349,2351],{"className":2350,"style":1096},[647],[569,2352,2353,2356],{"style":650},[569,2354],{"className":2355,"style":655},[654],[569,2357,2359],{"className":2358},[659,660,661,662],[569,2360,2362,2365],{"className":2361},[627,662],[569,2363,1062],{"className":2364},[627,631,662],[569,2366,1065],{"className":2367},[627,631,662]," sein. Die Beträge müssen übereinstimmen, also ",[569,2370,2372,2394],{"className":2371},[572],[569,2373,2375],{"className":2374},[576],[578,2376,2377],{"xmlns":580},[582,2378,2379,2391],{},[585,2380,2381,2383,2385],{},[591,2382,2042],{},[599,2384,601],{},[1161,2386,2387,2389],{},[591,2388,1048],{},[591,2390,738],{},[606,2392,2393],{"encoding":608},"s = \\sqrt[n]{r}",[569,2395,2397,2415],{"className":2396,"ariaHidden":614},[613],[569,2398,2400,2403,2406,2409,2412],{"className":2399},[618],[569,2401],{"className":2402,"style":802},[622],[569,2404,2042],{"className":2405},[627,631],[569,2407],{"className":2408,"style":670},[669],[569,2410,601],{"className":2411},[674],[569,2413],{"className":2414,"style":670},[669],[569,2416,2418,2421],{"className":2417},[618],[569,2419],{"className":2420,"style":1179},[622],[569,2422,2424,2450],{"className":2423},[627,1183],[569,2425,2427],{"className":2426},[1187],[569,2428,2430],{"className":2429},[639],[569,2431,2433],{"className":2432},[643],[569,2434,2436],{"className":2435,"style":1197},[647],[569,2437,2438,2441],{"style":1200},[569,2439],{"className":2440,"style":1204},[654],[569,2442,2444],{"className":2443},[659,660,1208,662],[569,2445,2447],{"className":2446},[627,662],[569,2448,738],{"className":2449},[627,631,662],[569,2451,2453,2486],{"className":2452},[639,1218],[569,2454,2456,2483],{"className":2455},[643],[569,2457,2459,2471],{"className":2458,"style":1225},[647],[569,2460,2462,2465],{"className":2461,"style":1230},[1229],[569,2463],{"className":2464,"style":1234},[654],[569,2466,2468],{"className":2467,"style":1238},[627],[569,2469,1048],{"className":2470,"style":1100},[627,631],[569,2472,2473,2476],{"style":1244},[569,2474],{"className":2475,"style":1234},[654],[569,2477,2479],{"className":2478,"style":1252},[1251],[1254,2480,2481],{"xmlns":1256,"width":1257,"height":1258,"viewBox":1259,"preserveAspectRatio":1260},[1262,2482],{"d":1264},[569,2484,1269],{"className":2485},[1268],[569,2487,2489],{"className":2488},[643],[569,2490,2492],{"className":2491,"style":1276},[647],[569,2493],{},". Die Winkel dürfen sich um Vielfache von ",[569,2496,2498,2514],{"className":2497},[572],[569,2499,2501],{"className":2500},[576],[578,2502,2503],{"xmlns":580},[582,2504,2505,2511],{},[585,2506,2507,2509],{},[595,2508,703],{},[591,2510,1304],{},[606,2512,2513],{"encoding":608},"2\\pi",[569,2515,2517],{"className":2516,"ariaHidden":614},[613],[569,2518,2520,2523,2526],{"className":2519},[618],[569,2521],{"className":2522,"style":684},[622],[569,2524,703],{"className":2525},[627],[569,2527,1304],{"className":2528,"style":1385},[627,631]," unterscheiden, also ",[569,2531,2533,2562],{"className":2532},[572],[569,2534,2536],{"className":2535},[576],[578,2537,2538],{"xmlns":580},[582,2539,2540,2559],{},[585,2541,2542,2544,2546,2548,2550,2553,2555,2557],{},[591,2543,738],{},[591,2545,2055],{},[599,2547,601],{},[591,2549,1065],{},[599,2551,2552],{},"+",[595,2554,703],{},[591,2556,1452],{},[591,2558,1304],{},[606,2560,2561],{"encoding":608},"n\\psi = \\varphi + 2k\\pi",[569,2563,2565,2586,2607],{"className":2564,"ariaHidden":614},[613],[569,2566,2568,2571,2574,2577,2580,2583],{"className":2567},[618],[569,2569],{"className":2570,"style":841},[622],[569,2572,738],{"className":2573},[627,631],[569,2575,2055],{"className":2576,"style":1385},[627,631],[569,2578],{"className":2579,"style":670},[669],[569,2581,601],{"className":2582},[674],[569,2584],{"className":2585,"style":670},[669],[569,2587,2589,2593,2596,2600,2604],{"className":2588},[618],[569,2590],{"className":2591,"style":2592},[622],"height:0.7778em;vertical-align:-0.1944em;",[569,2594,1065],{"className":2595},[627,631],[569,2597],{"className":2598,"style":2599},[669],"margin-right:0.2222em;",[569,2601,2552],{"className":2602},[2603],"mbin",[569,2605],{"className":2606,"style":2599},[669],[569,2608,2610,2613,2616,2619],{"className":2609},[618],[569,2611],{"className":2612,"style":1469},[622],[569,2614,703],{"className":2615},[627],[569,2617,1452],{"className":2618,"style":1473},[627,631],[569,2620,1304],{"className":2621,"style":1385},[627,631]," und damit ",[569,2624,2626,2658],{"className":2625},[572],[569,2627,2629],{"className":2628},[576],[578,2630,2631],{"xmlns":580},[582,2632,2633,2655],{},[585,2634,2635,2637,2639],{},[591,2636,2055],{},[599,2638,601],{},[1296,2640,2641,2653],{},[585,2642,2643,2645,2647,2649,2651],{},[591,2644,1065],{},[599,2646,2552],{},[595,2648,703],{},[591,2650,1452],{},[591,2652,1304],{},[591,2654,738],{},[606,2656,2657],{"encoding":608},"\\psi = \\frac{\\varphi + 2k\\pi}{n}",[569,2659,2661,2679],{"className":2660,"ariaHidden":614},[613],[569,2662,2664,2667,2670,2673,2676],{"className":2663},[618],[569,2665],{"className":2666,"style":841},[622],[569,2668,2055],{"className":2669,"style":1385},[627,631],[569,2671],{"className":2672,"style":670},[669],[569,2674,601],{"className":2675},[674],[569,2677],{"className":2678,"style":670},[669],[569,2680,2682,2686],{"className":2681},[618],[569,2683],{"className":2684,"style":2685},[622],"height:1.2772em;vertical-align:-0.345em;",[569,2687,2689,2692,2765],{"className":2688},[627],[569,2690],{"className":2691},[1326,1327],[569,2693,2695],{"className":2694},[1296],[569,2696,2698,2757],{"className":2697},[639,1218],[569,2699,2701,2754],{"className":2700},[643],[569,2702,2705,2719,2727],{"className":2703,"style":2704},[647],"height:0.9322em;",[569,2706,2707,2710],{"style":1343},[569,2708],{"className":2709,"style":1234},[654],[569,2711,2713],{"className":2712},[659,660,661,662],[569,2714,2716],{"className":2715},[627,662],[569,2717,738],{"className":2718},[627,631,662],[569,2720,2721,2724],{"style":1358},[569,2722],{"className":2723,"style":1234},[654],[569,2725],{"className":2726,"style":1366},[1365],[569,2728,2730,2733],{"style":2729},"top:-3.4461em;",[569,2731],{"className":2732,"style":1234},[654],[569,2734,2736],{"className":2735},[659,660,661,662],[569,2737,2739,2742,2745,2748,2751],{"className":2738},[627,662],[569,2740,1065],{"className":2741},[627,631,662],[569,2743,2552],{"className":2744},[2603,662],[569,2746,703],{"className":2747},[627,662],[569,2749,1452],{"className":2750,"style":1473},[627,631,662],[569,2752,1304],{"className":2753,"style":1385},[627,631,662],[569,2755,1269],{"className":2756},[1268],[569,2758,2760],{"className":2759},[643],[569,2761,2763],{"className":2762,"style":1395},[647],[569,2764],{},[569,2766],{"className":2767},[1401,1327],[560,2769,2771],{"id":2770},"beispiele","Beispiele",[565,2773,2774,2855,2856,2907,2908,2907,2960,3091],{},[569,2775,2777,2799],{"className":2776},[572],[569,2778,2780],{"className":2779},[576],[578,2781,2782],{"xmlns":580},[582,2783,2784,2796],{},[585,2785,2786,2792,2794],{},[588,2787,2788,2790],{},[591,2789,735],{},[595,2791,597],{},[599,2793,601],{},[595,2795,604],{},[606,2797,2798],{"encoding":608},"z^3 = 8",[569,2800,2802,2846],{"className":2801,"ariaHidden":614},[613],[569,2803,2805,2808,2837,2840,2843],{"className":2804},[618],[569,2806],{"className":2807,"style":623},[622],[569,2809,2811,2814],{"className":2810},[627],[569,2812,735],{"className":2813,"style":763},[627,631],[569,2815,2817],{"className":2816},[635],[569,2818,2820],{"className":2819},[639],[569,2821,2823],{"className":2822},[643],[569,2824,2826],{"className":2825,"style":623},[647],[569,2827,2828,2831],{"style":650},[569,2829],{"className":2830,"style":655},[654],[569,2832,2834],{"className":2833},[659,660,661,662],[569,2835,597],{"className":2836},[627,662],[569,2838],{"className":2839,"style":670},[669],[569,2841,601],{"className":2842},[674],[569,2844],{"className":2845,"style":670},[669],[569,2847,2849,2852],{"className":2848},[618],[569,2850],{"className":2851,"style":684},[622],[569,2853,604],{"className":2854},[627],": Hier ist ",[569,2857,2859,2877],{"className":2858},[572],[569,2860,2862],{"className":2861},[576],[578,2863,2864],{"xmlns":580},[582,2865,2866,2874],{},[585,2867,2868,2870,2872],{},[591,2869,1048],{},[599,2871,601],{},[595,2873,604],{},[606,2875,2876],{"encoding":608},"r = 8",[569,2878,2880,2898],{"className":2879,"ariaHidden":614},[613],[569,2881,2883,2886,2889,2892,2895],{"className":2882},[618],[569,2884],{"className":2885,"style":802},[622],[569,2887,1048],{"className":2888,"style":1100},[627,631],[569,2890],{"className":2891,"style":670},[669],[569,2893,601],{"className":2894},[674],[569,2896],{"className":2897,"style":670},[669],[569,2899,2901,2904],{"className":2900},[618],[569,2902],{"className":2903,"style":684},[622],[569,2905,604],{"className":2906},[627],", ",[569,2909,2911,2929],{"className":2910},[572],[569,2912,2914],{"className":2913},[576],[578,2915,2916],{"xmlns":580},[582,2917,2918,2926],{},[585,2919,2920,2922,2924],{},[591,2921,1065],{},[599,2923,601],{},[595,2925,828],{},[606,2927,2928],{"encoding":608},"\\varphi = 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= e^{i\\pi\u002F4} = \\frac{\\sqrt{2}}{2} + \\frac{\\sqrt{2}}{2}\\,i, \\qquad\nz_1 = e^{i \\cdot 5\\pi\u002F4} = -\\frac{\\sqrt{2}}{2} - \\frac{\\sqrt{2}}{2}\\,i",[569,4092,4094,4149,4201,4327,4503,4562,4686],{"className":4093,"ariaHidden":614},[613],[569,4095,4097,4100,4140,4143,4146],{"className":4096},[618],[569,4098],{"className":4099,"style":1524},[622],[569,4101,4103,4106],{"className":4102},[627],[569,4104,735],{"className":4105,"style":763},[627,631],[569,4107,4109],{"className":4108},[635],[569,4110,4112,4132],{"className":4111},[639,1218],[569,4113,4115,4129],{"className":4114},[643],[569,4116,4118],{"className":4117,"style":1543},[647],[569,4119,4120,4123],{"style":1546},[569,4121],{"className":4122,"style":655},[654],[569,4124,4126],{"className":4125},[659,660,661,662],[569,4127,828],{"className":4128},[627,662],[569,4130,1269],{"className":4131},[1268],[569,4133,4135],{"className":4134},[643],[569,4136,4138],{"className":4137,"style":1565},[647],[569,4139],{},[569,4141],{"className":4142,"style":670},[669],[569,4144,601],{"className":4145},[674],[569,4147],{"className":4148,"style":670},[669],[569,4150,4152,4155,4192,4195,4198],{"className":4151},[618],[569,4153],{"className":4154,"style":3362},[622],[569,4156,4158,4161],{"className":4157},[627],[569,4159,1057],{"className":4160},[627,631],[569,4162,4164],{"className":4163},[635],[569,4165,4167],{"className":4166},[639],[569,4168,4170],{"className":4169},[643],[569,4171,4173],{"className":4172,"style":3362},[647],[569,4174,4175,4178],{"style":3389},[569,4176],{"className":4177,"style":655},[654],[569,4179,4181],{"className":4180},[659,660,661,662],[569,4182,4184,4188],{"className":4183},[627,662],[569,4185,4187],{"className":4186,"style":1385},[627,631,662],"iπ",[569,4189,4191],{"className":4190},[627,662],"\u002F4",[569,4193],{"className":4194,"style":670},[669],[569,4196,601],{"className":4197},[674],[569,4199],{"className":4200,"style":670},[669],[569,4202,4204,4208,4318,4321,4324],{"className":4203},[618],[569,4205],{"className":4206,"style":4207},[622],"height:2.2702em;vertical-align:-0.686em;",[569,4209,4211,4214,4315],{"className":4210},[627],[569,4212],{"className":4213},[1326,1327],[569,4215,4217],{"className":4216},[1296],[569,4218,4220,4306],{"className":4219},[639,1218],[569,4221,4223,4303],{"className":4222},[643],[569,4224,4227,4239,4247],{"className":4225,"style":4226},[647],"height:1.5842em;",[569,4228,4230,4233],{"style":4229},"top:-2.314em;",[569,4231],{"className":4232,"style":1234},[654],[569,4234,4236],{"className":4235},[627],[569,4237,703],{"className":4238},[627],[569,4240,4241,4244],{"style":1358},[569,4242],{"className":4243,"style":1234},[654],[569,4245],{"className":4246,"style":1366},[1365],[569,4248,4250,4253],{"style":4249},"top:-3.677em;",[569,4251],{"className":4252,"style":1234},[654],[569,4254,4256],{"className":4255},[627],[569,4257,4259],{"className":4258},[627,1183],[569,4260,4262,4295],{"className":4261},[639,1218],[569,4263,4265,4292],{"className":4264},[643],[569,4266,4268,4280],{"className":4267,"style":3035},[647],[569,4269,4271,4274],{"className":4270,"style":1230},[1229],[569,4272],{"className":4273,"style":1234},[654],[569,4275,4277],{"className":4276,"style":1238},[627],[569,4278,703],{"className":4279},[627],[569,4281,4282,4285],{"style":3050},[569,4283],{"className":4284,"style":1234},[654],[569,4286,4288],{"className":4287,"style":1252},[1251],[1254,4289,4290],{"xmlns":1256,"width":1257,"height":1258,"viewBox":1259,"preserveAspectRatio":1260},[1262,4291],{"d":1264},[569,4293,1269],{"className":4294},[1268],[569,4296,4298],{"className":4297},[643],[569,4299,4301],{"className":4300,"style":3070},[647],[569,4302],{},[569,4304,1269],{"className":4305},[1268],[569,4307,4309],{"className":4308},[643],[569,4310,4313],{"className":4311,"style":4312},[647],"height:0.686em;",[569,4314],{},[569,4316],{"className":4317},[1401,1327],[569,4319],{"className":4320,"style":2599},[669],[569,4322,2552],{"className":4323},[2603],[569,4325],{"className":4326,"style":2599},[669],[569,4328,4330,4333,4439,4442,4445,4448,4451,4454,4494,4497,4500],{"className":4329},[618],[569,4331],{"className":4332,"style":4207},[622],[569,4334,4336,4339,4436],{"className":4335},[627],[569,4337],{"className":4338},[1326,1327],[569,4340,4342],{"className":4341},[1296],[569,4343,4345,4428],{"className":4344},[639,1218],[569,4346,4348,4425],{"className":4347},[643],[569,4349,4351,4362,4370],{"className":4350,"style":4226},[647],[569,4352,4353,4356],{"style":4229},[569,4354],{"className":4355,"style":1234},[654],[569,4357,4359],{"className":4358},[627],[569,4360,703],{"className":4361},[627],[569,4363,4364,4367],{"style":1358},[569,4365],{"className":4366,"style":1234},[654],[569,4368],{"className":4369,"style":1366},[1365],[569,4371,4372,4375],{"style":4249},[569,4373],{"className":4374,"style":1234},[654],[569,4376,4378],{"className":4377},[627],[569,4379,4381],{"className":4380},[627,1183],[569,4382,4384,4417],{"className":4383},[639,1218],[569,4385,4387,4414],{"className":4386},[643],[569,4388,4390,4402],{"className":4389,"style":3035},[647],[569,4391,4393,4396],{"class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\\sqrt{2}\\,i",[569,5542,5544,5617,5682],{"className":5543,"ariaHidden":614},[613],[569,5545,5547,5551,5608,5611,5614],{"className":5546},[618],[569,5548],{"className":5549,"style":5550},[622],"height:0.7167em;vertical-align:-0.2861em;",[569,5552,5554,5557],{"className":5553},[627],[569,5555,735],{"className":5556,"style":763},[627,631],[569,5558,5560],{"className":5559},[635],[569,5561,5563,5599],{"className":5562},[639,1218],[569,5564,5566,5596],{"className":5565},[643],[569,5567,5569],{"className":5568,"style":1543},[647],[569,5570,5571,5574],{"style":1546},[569,5572],{"className":5573,"style":655},[654],[569,5575,5577],{"className":5576},[659,660,661,662],[569,5578,5580,5583,5586,5590,5593],{"className":5579},[627,662],[569,5581,828],{"className":5582},[627,662],[569,5584,3121],{"className":5585},[3299,662],[569,5587,5514],{"className":5588},[5589,662],"minner",[569,5591,3121],{"className":5592},[3299,662],[569,5594,597],{"className":5595},[627,662],[569,5597,1269],{"className":5598},[1268],[569,5600,5602],{"className":5601},[643],[569,5603,5606],{"className":5604,"style":5605},[647],"height:0.2861em;",[569,5607],{},[569,5609],{"className":5610,"style":670},[669],[569,5612,601],{"className":5613},[674],[569,5615],{"className":5616,"style":670},[669],[569,5618,5620,5623,5626,5673,5676,5679],{"className":5619},[618],[569,5621],{"className":5622,"style":3659},[622],[569,5624,5523],{"className":5625},[627],[569,5627,5629],{"className":5628},[627,1183],[569,5630,5632,5665],{"className":5631},[639,1218],[569,5633,5635,5662],{"className":5634},[643],[569,5636,5638,5650],{"className":5637,"style":3465},[647],[569,5639,5641,5644],{"className":5640,"style":1230},[1229],[569,5642],{"className":5643,"style":1234},[654],[569,5645,5647],{"className":5646,"style":1238},[627],[569,5648,703],{"className":5649},[627],[569,5651,5652,5655],{"style":3480},[569,5653],{"className":5654,"style":1234},[654],[569,5656,5658],{"className":5657,"style":1252},[1251],[1254,5659,5660],{"xmlns":1256,"width":1257,"height":1258,"viewBox":1259,"preserveAspectRatio":1260},[1262,5661],{"d":1264},[569,5663,1269],{"className":5664},[1268],[569,5666,5668],{"className":5667},[643],[569,5669,5671],{"className":5670,"style":3500},[647],[569,5672],{},[569,5674],{"className":5675,"style":2599},[669],[569,5677,5523],{"className":5678},[2603],[569,5680],{"className":5681,"style":2599},[669],[569,5683,5685,5688,5735,5738],{"className":5684},[618],[569,5686],{"className":5687,"style":3659},[622],[569,5689,5691],{"className":5690},[627,1183],[569,5692,5694,5727],{"className":5693},[639,1218],[569,5695,5697,5724],{"className":5696},[643],[569,5698,5700,5712],{"className":5699,"style":3465},[647],[569,5701,5703,5706],{"className":5702,"style":1230},[1229],[569,5704],{"className":5705,"style":1234},[654],[569,5707,5709],{"className":5708,"style":1238},[627],[569,5710,703],{"className":5711},[627],[569,5713,5714,5717],{"style":3480},[569,5715],{"className":5716,"style":1234},[654],[569,5718,5720],{"className":5719,"style":1252},[1251],[1254,5721,5722],{"xmlns":1256,"width":1257,"height":1258,"viewBox":1259,"preserveAspectRatio":1260},[1262,5723],{"d":1264},[569,5725,1269],{"className":5726},[1268],[569,5728,5730],{"className":5729},[643],[569,5731,5733],{"className":5732,"style":3500},[647],[569,5734],{},[569,5736],{"className":5737,"style":1104},[669],[569,5739,1062],{"className":5740},[627,631],[560,5742,5744],{"id":5743},"typische-fehler","Typische Fehler",[1142,5746,5747,5882,5925,6117],{},[1145,5748,5749,5750,5830,5831,997],{},"Nur die reelle Lösung angeben. ",[569,5751,5753,5774],{"className":5752},[572],[569,5754,5756],{"className":5755},[576],[578,5757,5758],{"xmlns":580},[582,5759,5760,5772],{},[585,5761,5762,5768,5770],{},[588,5763,5764,5766],{},[591,5765,735],{},[595,5767,597],{},[599,5769,601],{},[595,5771,604],{},[606,5773,2798],{"encoding":608},[569,5775,5777,5821],{"className":5776,"ariaHidden":614},[613],[569,5778,5780,5783,5812,5815,5818],{"className":5779},[618],[569,5781],{"className":5782,"style":623},[622],[569,5784,5786,5789],{"className":5785},[627],[569,5787,735],{"className":5788,"style":763},[627,631],[569,5790,5792],{"className":5791},[635],[569,5793,5795],{"className":5794},[639],[569,5796,5798],{"className":5797},[643],[569,5799,5801],{"className":5800,"style":623},[647],[569,5802,5803,5806],{"style":650},[569,5804],{"className":5805,"style":655},[654],[569,5807,5809],{"className":5808},[659,660,661,662],[569,5810,597],{"className":5811},[627,662],[569,5813],{"className":5814,"style":670},[669],[569,5816,601],{"className":5817},[674],[569,5819],{"className":5820,"style":670},[669],[569,5822,5824,5827],{"className":5823},[618],[569,5825],{"className":5826,"style":684},[622],[569,5828,604],{"className":5829},[627]," hat drei komplexe Lösungen, nicht nur ",[569,5832,5834,5852],{"className":5833},[572],[569,5835,5837],{"className":5836},[576],[578,5838,5839],{"xmlns":580},[582,5840,5841,5849],{},[585,5842,5843,5845,5847],{},[591,5844,735],{},[599,5846,601],{},[595,5848,703],{},[606,5850,5851],{"encoding":608},"z = 2",[569,5853,5855,5873],{"className":5854,"ariaHidden":614},[613],[569,5856,5858,5861,5864,5867,5870],{"className":5857},[618],[569,5859],{"className":5860,"style":802},[622],[569,5862,735],{"className":5863,"style":763},[627,631],[569,5865],{"className":5866,"style":670},[669],[569,5868,601],{"className":5869},[674],[569,5871],{"className":5872,"style":670},[669],[569,5874,5876,5879],{"className":5875},[618],[569,5877],{"className":5878,"style":684},[622],[569,5880,703],{"className":5881},[627],[1145,5883,5884,5885,5924],{},"Den Summanden ",[569,5886,5888,5906],{"className":5887},[572],[569,5889,5891],{"className":5890},[576],[578,5892,5893],{"xmlns":580},[582,5894,5895,5903],{},[585,5896,5897,5899,5901],{},[595,5898,703],{},[591,5900,1452],{},[591,5902,1304],{},[606,5904,5905],{"encoding":608},"2k\\pi",[569,5907,5909],{"className":5908,"ariaHidden":614},[613],[569,5910,5912,5915,5918,5921],{"className":5911},[618],[569,5913],{"className":5914,"style":1469},[622],[569,5916,703],{"className":5917},[627],[569,5919,1452],{"className":5920,"style":1473},[627,631],[569,5922,1304],{"className":5923,"style":1385},[627,631]," vergessen. Dann erhält man nur eine einzige Lösung.",[1145,5926,5927,5928,5966,5967,5995,5996,6025,6026,6087,6088,6116],{},"Nur ",[569,5929,5931,5948],{"className":5930},[572],[569,5932,5934],{"className":5933},[576],[578,5935,5936],{"xmlns":580},[582,5937,5938,5946],{},[585,5939,5940,5942,5944],{},[595,5941,703],{},[591,5943,1452],{},[591,5945,1304],{},[606,5947,5905],{"encoding":608},[569,5949,5951],{"className":5950,"ariaHidden":614},[613],[569,5952,5954,5957,5960,5963],{"className":5953},[618],[569,5955],{"className":5956,"style":1469},[622],[569,5958,703],{"className":5959},[627],[569,5961,1452],{"className":5962,"style":1473},[627,631],[569,5964,1304],{"className":5965,"style":1385},[627,631]," durch ",[569,5968,5970,5983],{"className":5969},[572],[569,5971,5973],{"className":5972},[576],[578,5974,5975],{"xmlns":580},[582,5976,5977,5981],{},[585,5978,5979],{},[591,5980,738],{},[606,5982,738],{"encoding":608},[569,5984,5986],{"className":5985,"ariaHidden":614},[613],[569,5987,5989,5992],{"className":5988},[618],[569,5990],{"className":5991,"style":802},[622],[569,5993,738],{"className":5994},[627,631]," teilen und ",[569,5997,5999,6013],{"className":5998},[572],[569,6000,6002],{"className":6001},[576],[578,6003,6004],{"xmlns":580},[582,6005,6006,6010],{},[585,6007,6008],{},[591,6009,1065],{},[606,6011,6012],{"encoding":608},"\\varphi",[569,6014,6016],{"className":6015,"ariaHidden":614},[613],[569,6017,6019,6022],{"className":6018},[618],[569,6020],{"className":6021,"style":2938},[622],[569,6023,1065],{"className":6024},[627,631]," stehen lassen. Der ganze Winkel ",[569,6027,6029,6051],{"className":6028},[572],[569,6030,6032],{"className":6031},[576],[578,6033,6034],{"xmlns":580},[582,6035,6036,6048],{},[585,6037,6038,6040,6042,6044,6046],{},[591,6039,1065],{},[599,6041,2552],{},[595,6043,703],{},[591,6045,1452],{},[591,6047,1304],{},[606,6049,6050],{"encoding":608},"\\varphi + 2k\\pi",[569,6052,6054,6072],{"className":6053,"ariaHidden":614},[613],[569,6055,6057,6060,6063,6066,6069],{"className":6056},[618],[569,6058],{"className":6059,"style":2592},[622],[569,6061,1065],{"className":6062},[627,631],[569,6064],{"className":6065,"style":2599},[669],[569,6067,2552],{"className":6068},[2603],[569,6070],{"className":6071,"style":2599},[669],[569,6073,6075,6078,6081,6084],{"className":6074},[618],[569,6076],{"className":6077,"style":1469},[622],[569,6079,703],{"className":6080},[627],[569,6082,1452],{"className":6083,"style":1473},[627,631],[569,6085,1304],{"className":6086,"style":1385},[627,631]," wird durch ",[569,6089,6091,6104],{"className":6090},[572],[569,6092,6094],{"className":6093},[576],[578,6095,6096],{"xmlns":580},[582,6097,6098,6102],{},[585,6099,6100],{},[591,6101,738],{},[606,6103,738],{"encoding":608},[569,6105,6107],{"className":6106,"ariaHidden":614},[613],[569,6108,6110,6113],{"className":6109},[618],[569,6111],{"className":6112,"style":802},[622],[569,6114,738],{"className":6115},[627,631]," geteilt.",[1145,6118,6119,6120,6148,6149,6177,6178,6263,6264,6388,6389,997],{},"Den Betrag durch ",[569,6121,6123,6136],{"className":6122},[572],[569,6124,6126],{"className":6125},[576],[578,6127,6128],{"xmlns":580},[582,6129,6130,6134],{},[585,6131,6132],{},[591,6133,738],{},[606,6135,738],{"encoding":608},[569,6137,6139],{"className":6138,"ariaHidden":614},[613],[569,6140,6142,6145],{"className":6141},[618],[569,6143],{"className":6144,"style":802},[622],[569,6146,738],{"className":6147},[627,631]," teilen statt die ",[569,6150,6152,6165],{"className":6151},[572],[569,6153,6155],{"className":6154},[576],[578,6156,6157],{"xmlns":580},[582,6158,6159,6163],{},[585,6160,6161],{},[591,6162,738],{},[606,6164,738],{"encoding":608},[569,6166,6168],{"className":6167,"ariaHidden":614},[613],[569,6169,6171,6174],{"className":6170},[618],[569,6172],{"className":6173,"style":802},[622],[569,6175,738],{"className":6176},[627,631],"-te Wurzel zu ziehen: Für ",[569,6179,6181,6204],{"className":6180},[572],[569,6182,6184],{"className":6183},[576],[578,6185,6186],{"xmlns":580},[582,6187,6188,6202],{},[585,6189,6190,6196,6198,6200],{},[588,6191,6192,6194],{},[591,6193,735],{},[595,6195,3202],{},[599,6197,601],{},[599,6199,3160],{},[595,6201,4830],{},[606,6203,4833],{"encoding":608},[569,6205,6207,6251],{"className":6206,"ariaHidden":614},[613],[569,6208,6210,6213,6242,6245,6248],{"className":6209},[618],[569,6211],{"className":6212,"style":623},[622],[569,6214,6216,6219],{"className":6215},[627],[569,6217,735],{"className":6218,"style":763},[627,631],[569,6220,6222],{"className":6221},[635],[569,6223,6225],{"className":6224},[639],[569,6226,6228],{"className":6227},[643],[569,6229,6231],{"className":6230,"style":623},[647],[569,6232,6233,6236],{"style":650},[569,6234],{"className":6235,"style":655},[654],[569,6237,6239],{"className":6238},[659,660,661,662],[569,6240,3202],{"className":6241},[627,662],[569,6243],{"className":6244,"style":670},[669],[569,6246,601],{"className":6247},[674],[569,6249],{"className":6250,"style":670},[669],[569,6252,6254,6257,6260],{"className":6253},[618],[569,6255],{"className":6256,"style":3430},[622],[569,6258,3160],{"className":6259},[627],[569,6261,4830],{"className":6262},[627]," ist der Betrag der Lösungen ",[569,6265,6267,6288],{"className":6266},[572],[569,6268,6270],{"className":6269},[576],[578,6271,6272],{"xmlns":580},[582,6273,6274,6286],{},[585,6275,6276,6282,6284],{},[1161,6277,6278,6280],{},[595,6279,4830],{},[595,6281,3202],{},[599,6283,601],{},[595,6285,703],{},[606,6287,5019],{"encoding":608},[569,6289,6291,6379],{"className":6290,"ariaHidden":614},[613],[569,6292,6294,6297,6370,6373,6376],{"className":6293},[618],[569,6295],{"className":6296,"style":2994},[622],[569,6298,6300,6326],{"className":6299},[627,1183],[569,6301,6303],{"className":6302},[1187],[569,6304,6306],{"className":6305},[639],[569,6307,6309],{"className":6308},[643],[569,6310,6312],{"className":6311,"style":3010},[647],[569,6313,6314,6317],{"style":3013},[569,6315],{"className":6316,"style":1204},[654],[569,6318,6320],{"className":6319},[659,660,1208,662],[569,6321,6323],{"className":6322},[627,662],[569,6324,3202],{"className":6325},[627,662],[569,6327,6329,6362],{"className":6328},[639,1218],[569,6330,6332,6359],{"className":6331},[643],[569,6333,6335,6347],{"className":6334,"style":3035},[647],[569,6336,6338,6341],{"className":6337,"style":1230},[1229],[569,6339],{"className":6340,"style":1234},[654],[569,6342,6344],{"className":6343,"style":1238},[627],[569,6345,4830],{"className":6346},[627],[569,6348,6349,6352],{"style":3050},[569,6350],{"className":6351,"style":1234},[654],[569,6353,6355],{"className":6354,"style":1252},[1251],[1254,6356,6357],{"xmlns":1256,"width":1257,"height":1258,"viewBox":1259,"preserveAspectRatio":1260},[1262,6358],{"d":1264},[569,6360,1269],{"className":6361},[1268],[569,6363,6365],{"className":6364},[643],[569,6366,6368],{"className":6367,"style":3070},[647],[569,6369],{},[569,6371],{"className":6372,"style":670},[669],[569,6374,601],{"className":6375},[674],[569,6377],{"className":6378,"style":670},[669],[569,6380,6382,6385],{"className":6381},[618],[569,6383],{"className":6384,"style":684},[622],[569,6386,703],{"className":6387},[627],", nicht ",[569,6390,6392,6405],{"className":6391},[572],[569,6393,6395],{"className":6394},[576],[578,6396,6397],{"xmlns":580},[582,6398,6399,6403],{},[585,6400,6401],{},[595,6402,3202],{},[606,6404,3202],{"encoding":608},[569,6406,6408],{"className":6407,"ariaHidden":614},[613],[569,6409,6411,6414],{"className":6410},[618],[569,6412],{"className":6413,"style":684},[622],[569,6415,3202],{"className":6416},[627],{"title":6418,"searchDepth":6419,"depth":6419,"links":6420},"",2,[6421,6422,6423,6424],{"id":562,"depth":6419,"text":563},{"id":2019,"depth":6419,"text":2020},{"id":2770,"depth":6419,"text":2771},{"id":5743,"depth":6419,"text":5744},[6426,6432,6436,6438,6441,6444,6446,6448,6450,6452,6455,6457,6459,6461,6463,6465,6468,6471,6473,6475],{"lhs":6427,"rhs":6428,"where":6429},"re((nthRoot(r, n) * exp(i*(x + 2*k*pi)\u002Fn))^n)","r * cos(x)",{"n":6430,"k":6431},5,3,{"lhs":6433,"rhs":6434,"where":6435},"im((nthRoot(r, n) * exp(i*(x + 2*k*pi)\u002Fn))^n)","r * sin(x)",{"n":6430,"k":6431},{"lhs":6437,"rhs":703},"nthRoot(8, 3)",{"lhs":6439,"rhs":6440},"re(2 * exp(i*2*pi\u002F3))","-1",{"lhs":6442,"rhs":6443},"im(2 * exp(i*2*pi\u002F3))","sqrt(3)",{"lhs":6445,"rhs":604},"re((-1 + sqrt(3)*i)^3)",{"lhs":6447,"rhs":828},"im((-1 + sqrt(3)*i)^3)",{"lhs":6449,"rhs":604},"re((-1 - sqrt(3)*i)^3)",{"lhs":6451,"rhs":828},"im((-1 - sqrt(3)*i)^3)",{"lhs":6453,"rhs":6454},"re(exp(i*pi\u002F4))","sqrt(2)\u002F2",{"lhs":6456,"rhs":828},"re((sqrt(2)\u002F2 + sqrt(2)\u002F2*i)^2)",{"lhs":6458,"rhs":1618},"im((sqrt(2)\u002F2 + sqrt(2)\u002F2*i)^2)",{"lhs":6460,"rhs":828},"re((-sqrt(2)\u002F2 - sqrt(2)\u002F2*i)^2)",{"lhs":6462,"rhs":1618},"im((-sqrt(2)\u002F2 - sqrt(2)\u002F2*i)^2)",{"lhs":6464,"rhs":703},"nthRoot(16, 4)",{"lhs":6466,"rhs":6467},"re(2 * exp(i*pi\u002F4))","sqrt(2)",{"lhs":6469,"rhs":6470},"re((sqrt(2) + sqrt(2)*i)^4)","-16",{"lhs":6472,"rhs":828},"im((sqrt(2) + sqrt(2)*i)^4)",{"lhs":6474,"rhs":6470},"re((-sqrt(2) + sqrt(2)*i)^4)",{"lhs":6476,"rhs":828},"im((-sqrt(2) - sqrt(2)*i)^4)","w = r\\,e^{i\\varphi},\\ r > 0,\\ n \\in \\mathbb{N},\\ n \\geq 1,\\ k = 0, 1, \\ldots, n-1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>w\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>r\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmsup>\u003Cmi>e\u003C\u002Fmi>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmi>φ\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">w = r\\,e^{i\\varphi},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0269em;\">w\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0191em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">e\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8247em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">φ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>r\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">r > 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\in \\mathbb{N},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">N\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\geq 1,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k = 0, 1, \\ldots, n-1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","complex-roots","z_k = \\sqrt[n]{r}\\,\\Bigl(\\cos\\frac{\\varphi + 2k\\pi}{n} + i\\sin\\frac{\\varphi + 2k\\pi}{n}\\Bigr)","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>z\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmroot>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmroot>\u003Cmtext> \u003C\u002Fmtext>\u003Cmo fence=\"true\" stretchy=\"true\" minsize=\"1.8em\" maxsize=\"1.8em\">(\u003C\u002Fmo>\u003Cmi>cos\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>φ\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>k\u003C\u002Fmi>\u003Cmi>π\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>i\u003C\u002Fmi>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>φ\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>k\u003C\u002Fmi>\u003Cmi>π\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo fence=\"true\" stretchy=\"true\" minsize=\"1.8em\" maxsize=\"1.8em\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">z_k = \\sqrt[n]{r}\\,\\Bigl(\\cos\\frac{\\varphi + 2k\\pi}{n} + i\\sin\\frac{\\varphi + 2k\\pi}{n}\\Bigr)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.044em;\">z\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0574em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord sqrt\">\u003Cspan class=\"katex-root\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6103em;\">\u003Cspan style=\"top:-2.895em;\">\u003Cspan class=\"pstrut\" style=\"height:2.5em;\">\u003C\u002Fspan>\u003Cspan 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class=\"delimsizing size2\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mop\">cos\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">φ\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0574em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">i\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">φ\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"delimsizing size2\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Falgebra\u002Fn-te-wurzel-komplexe-zahl",[],[6490,6491,6492],"de-moivre","polar-form","euler-formula",{"title":548,"description":6418},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fn-te-wurzel-komplexe-zahl","Die Gleichung zⁿ = w hat für w ≠ 0 genau n verschiedene komplexe Lösungen, die ein regelmäßiges n-Eck bilden.",[6497,6498,6499,6500,6501],"komplexe zahlen","wurzel","einheitswurzeln","polarform","kreisteilung",[6503,6506,6509,6512,6515,6518,6522],{"symbol":743,"meaning":6504,"symbolHtml":6505},"komplexe Zahl, deren Wurzeln gesucht sind (Lösungen von zⁿ = 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style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">φ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":738,"meaning":6513,"symbolHtml":6514},"Wurzelexponent","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1452,"meaning":6516,"symbolHtml":6517},"Nummer der Lösung","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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encoding=\"application\u002Fx-tex\">z_k\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.044em;\">z\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan 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