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|w|",[568,1120,1122,1143,1165,1189],{"className":1121,"ariaHidden":615},[614],[568,1123,1125,1128,1131,1134,1137,1140],{"className":1124},[619],[568,1126],{"className":1127,"style":714},[623],[568,1129,696],{"className":1130},[628],[568,1132,589],{"className":1133,"style":630},[628,629],[568,1135],{"className":1136,"style":656},[634],[568,1138,1094],{"className":1139},[660],[568,1141],{"className":1142,"style":656},[634],[568,1144,1146,1149,1153,1156,1159,1162],{"className":1145},[619],[568,1147],{"className":1148,"style":714},[623],[568,1150,1097],{"className":1151,"style":1152},[628,629],"margin-right:0.0269em;",[568,1154,696],{"className":1155},[628],[568,1157],{"className":1158,"style":635},[634],[568,1160,593],{"className":1161},[639],[568,1163],{"className":1164,"style":635},[634],[568,1166,1168,1171,1174,1177,1180,1183,1186],{"className":1167},[619],[568,1169],{"className":1170,"style":714},[623],[568,1172,696],{"className":1173},[628],[568,1175,589],{"className":1176,"style":630},[628,629],[568,1178,696],{"className":1179},[628],[568,1181],{"className":1182,"style":656},[634],[568,1184,1094],{"className":1185},[660],[568,1187],{"className":1188,"style":656},[634],[568,1190,1192,1195,1198,1201],{"className":1191},[619],[568,1193],{"className":1194,"style":714},[623],[568,1196,696],{"className":1197},[628],[568,1199,1097],{"className":1200,"style":1152},[628,629],[568,1202,696],{"className":1203},[628]," und ",[568,1206,1208,1253],{"className":1207},[571],[568,1209,1211],{"className":1210},[575],[577,1212,1213],{"xmlns":579},[581,1214,1215,1250],{},[584,1216,1217,1230,1232],{},[584,1218,1219,1221,1228],{},[591,1220,696],{"fence":615},[1222,1223,1224,1226],"mfrac",{},[587,1225,589],{},[587,1227,1097],{},[591,1229,696],{"fence":615},[591,1231,593],{},[1222,1233,1234,1242],{},[584,1235,1236,1238,1240],{},[587,1237,696],{"mathvariant":764},[587,1239,589],{},[587,1241,696],{"mathvariant":764},[584,1243,1244,1246,1248],{},[587,1245,696],{"mathvariant":764},[587,1247,1097],{},[587,1249,696],{"mathvariant":764},[607,1251,1252],{"encoding":609},"\\left|\\frac{z}{w}\\right| = \\frac{|z|}{|w|}",[568,1254,1256,1452],{"className":1255,"ariaHidden":615},[614],[568,1257,1259,1263,1443,1446,1449],{"className":1258},[619],[568,1260],{"className":1261,"style":1262},[623],"height:1.2em;vertical-align:-0.35em;",[568,1264,1267,1325,1406],{"className":1265},[1266],"minner",[568,1268,1270],{"className":1269},[718],[568,1271,1275],{"className":1272},[1273,1274],"delimsizing","mult",[568,1276,1280,1316],{"className":1277},[1278,1279],"vlist-t","vlist-t2",[568,1281,1284,1311],{"className":1282},[1283],"vlist-r",[568,1285,1289],{"className":1286,"style":1288},[1287],"vlist","height:0.85em;",[568,1290,1292,1297],{"style":1291},"top:-2.85em;",[568,1293],{"className":1294,"style":1296},[1295],"pstrut","height:3.2em;",[568,1298,1300],{"style":1299},"width:0.333em;height:1.2em;",[1301,1302,1307],"svg",{"xmlns":1303,"width":1304,"height":1305,"viewBox":1306},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","0.333em","1.2em","0 0 333 1200",[1308,1309],"path",{"d":1310},"M145 15 v585 v0 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v0 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v0 v585 h43z",[568,1312,1315],{"className":1313},[1314],"vlist-s","​",[568,1317,1319],{"className":1318},[1283],[568,1320,1323],{"className":1321,"style":1322},[1287],"height:0.35em;",[568,1324],{},[568,1326,1328,1332,1403],{"className":1327},[628],[568,1329],{"className":1330},[718,1331],"nulldelimiter",[568,1333,1335],{"className":1334},[1222],[568,1336,1338,1394],{"className":1337},[1278,1279],[568,1339,1341,1391],{"className":1340},[1283],[568,1342,1345,1365,1376],{"className":1343,"style":1344},[1287],"height:0.6954em;",[568,1346,1348,1352],{"style":1347},"top:-2.655em;",[568,1349],{"className":1350,"style":1351},[1295],"height:3em;",[568,1353,1359],{"className":1354},[1355,1356,1357,1358],"sizing","reset-size6","size3","mtight",[568,1360,1362],{"className":1361},[628,1358],[568,1363,1097],{"className":1364,"style":1152},[628,629,1358],[568,1366,1368,1371],{"style":1367},"top:-3.23em;",[568,1369],{"className":1370,"style":1351},[1295],[568,1372],{"className":1373,"style":1375},[1374],"frac-line","border-bottom-width:0.04em;",[568,1377,1379,1382],{"style":1378},"top:-3.394em;",[568,1380],{"className":1381,"style":1351},[1295],[568,1383,1385],{"className":1384},[1355,1356,1357,1358],[568,1386,1388],{"className":1387},[628,1358],[568,1389,589],{"className":1390,"style":630},[628,629,1358],[568,1392,1315],{"className":1393},[1314],[568,1395,1397],{"className":1396},[1283],[568,1398,1401],{"className":1399,"style":1400},[1287],"height:0.345em;",[568,1402],{},[568,1404],{"className":1405},[743,1331],[568,1407,1409],{"className":1408},[743],[568,1410,1412],{"className":1411},[1273,1274],[568,1413,1415,1435],{"className":1414},[1278,1279],[568,1416,1418,1432],{"className":1417},[1283],[568,1419,1421],{"className":1420,"style":1288},[1287],[568,1422,1423,1426],{"style":1291},[568,1424],{"className":1425,"style":1296},[1295],[568,1427,1428],{"style":1299},[1301,1429,1430],{"xmlns":1303,"width":1304,"height":1305,"viewBox":1306},[1308,1431],{"d":1310},[568,1433,1315],{"className":1434},[1314],[568,1436,1438],{"className":1437},[1283],[568,1439,1441],{"className":1440,"style":1322},[1287],[568,1442],{},[568,1444],{"className":1445,"style":635},[634],[568,1447,593],{"className":1448},[639],[568,1450],{"className":1451,"style":635},[634],[568,1453,1455,1459],{"className":1454},[619],[568,1456],{"className":1457,"style":1458},[623],"height:1.53em;vertical-align:-0.52em;",[568,1460,1462,1465,1539],{"className":1461},[628],[568,1463],{"className":1464},[718,1331],[568,1466,1468],{"className":1467},[1222],[568,1469,1471,1530],{"className":1470},[1278,1279],[568,1472,1474,1527],{"className":1473},[1283],[568,1475,1478,1498,1506],{"className":1476,"style":1477},[1287],"height:1.01em;",[568,1479,1480,1483],{"style":1347},[568,1481],{"className":1482,"style":1351},[1295],[568,1484,1486],{"className":1485},[1355,1356,1357,1358],[568,1487,1489,1492,1495],{"className":1488},[628,1358],[568,1490,696],{"className":1491},[628,1358],[568,1493,1097],{"className":1494,"style":1152},[628,629,1358],[568,1496,696],{"className":1497},[628,1358],[568,1499,1500,1503],{"style":1367},[568,1501],{"className":1502,"style":1351},[1295],[568,1504],{"className":1505,"style":1375},[1374],[568,1507,1509,1512],{"style":1508},"top:-3.485em;",[568,1510],{"className":1511,"style":1351},[1295],[568,1513,1515],{"className":1514},[1355,1356,1357,1358],[568,1516,1518,1521,1524],{"className":1517},[628,1358],[568,1519,696],{"className":1520},[628,1358],[568,1522,589],{"className":1523,"style":630},[628,629,1358],[568,1525,696],{"className":1526},[628,1358],[568,1528,1315],{"className":1529},[1314],[568,1531,1533],{"className":1532},[1283],[568,1534,1537],{"className":1535,"style":1536},[1287],"height:0.52em;",[568,1538],{},[568,1540],{"className":1541},[743,1331]," für ",[568,1544,1546,1565],{"className":1545},[571],[568,1547,1549],{"className":1548},[575],[577,1550,1551],{"xmlns":579},[581,1552,1553,1562],{},[584,1554,1555,1557,1560],{},[587,1556,1097],{},[591,1558,1559],{"mathvariant":764},"≠",[822,1561,824],{},[607,1563,1564],{"encoding":609},"w \\neq 0",[568,1566,1568,1627],{"className":1567,"ariaHidden":615},[614],[568,1569,1571,1575,1578,1581,1624],{"className":1570},[619],[568,1572],{"className":1573,"style":1574},[623],"height:0.8889em;vertical-align:-0.1944em;",[568,1576,1097],{"className":1577,"style":1152},[628,629],[568,1579],{"className":1580,"style":635},[634],[568,1582,1584,1617,1621],{"className":1583},[639],[568,1585,1587],{"className":1586},[639],[568,1588,1591],{"className":1589},[628,1590],"vbox",[568,1592,1595],{"className":1593},[1594],"thinbox",[568,1596,1599,1602,1613],{"className":1597},[1598],"rlap",[568,1600],{"className":1601,"style":1574},[623],[568,1603,1606],{"className":1604},[1605],"inner",[568,1607,1609],{"className":1608},[628],[568,1610,1612],{"className":1611},[639],"",[568,1614],{"className":1615},[1616],"fix",[568,1618],{"className":1619},[634,1620],"nobreak",[568,1622,593],{"className":1623},[639],[568,1625],{"className":1626,"style":635},[634],[568,1628,1630,1633],{"className":1629},[619],[568,1631],{"className":1632,"style":861},[623],[568,1634,824],{"className":1635},[628],[798,1637,1638,1798,1799,979],{},[568,1639,1641,1679],{"className":1640},[571],[568,1642,1644],{"className":1643},[575],[577,1645,1646],{"xmlns":579},[581,1647,1648,1676],{},[584,1649,1650,1652,1654,1662,1664,1666,1668],{},[587,1651,696],{"mathvariant":764},[587,1653,589],{},[1655,1656,1657,1659],"msup",{},[587,1658,696],{"mathvariant":764},[822,1660,1661],{},"2",[591,1663,593],{},[587,1665,589],{},[591,1667,1094],{},[1669,1670,1671,1673],"mover",{"accent":615},[587,1672,589],{},[591,1674,1675],{"stretchy":615},"‾",[607,1677,1678],{"encoding":609},"|z|^2 = z \\cdot \\overline{z}",[568,1680,1682,1737,1756],{"className":1681,"ariaHidden":615},[614],[568,1683,1685,1689,1692,1695,1728,1731,1734],{"className":1684},[619],[568,1686],{"className":1687,"style":1688},[623],"height:1.0641em;vertical-align:-0.25em;",[568,1690,696],{"className":1691},[628],[568,1693,589],{"className":1694,"style":630},[628,629],[568,1696,1698,1701],{"className":1697},[628],[568,1699,696],{"className":1700},[628],[568,1702,1705],{"className":1703},[1704],"msupsub",[568,1706,1708],{"className":1707},[1278],[568,1709,1711],{"className":1710},[1283],[568,1712,1715],{"className":1713,"style":1714},[1287],"height:0.8141em;",[568,1716,1718,1722],{"style":1717},"top:-3.063em;margin-right:0.05em;",[568,1719],{"className":1720,"style":1721},[1295],"height:2.7em;",[568,1723,1725],{"className":1724},[1355,1356,1357,1358],[568,1726,1661],{"className":1727},[628,1358],[568,1729],{"className":1730,"style":635},[634],[568,1732,593],{"className":1733},[639],[568,1735],{"className":1736,"style":635},[634],[568,1738,1740,1744,1747,1750,1753],{"className":1739},[619],[568,1741],{"className":1742,"style":1743},[623],"height:0.4445em;",[568,1745,589],{"className":1746,"style":630},[628,629],[568,1748],{"className":1749,"style":656},[634],[568,1751,1094],{"className":1752},[660],[568,1754],{"className":1755,"style":656},[634],[568,1757,1759,1763],{"className":1758},[619],[568,1760],{"className":1761,"style":1762},[623],"height:0.6306em;",[568,1764,1767],{"className":1765},[628,1766],"overline",[568,1768,1770],{"className":1769},[1278],[568,1771,1773],{"className":1772},[1283],[568,1774,1776,1788],{"className":1775,"style":1762},[1287],[568,1777,1779,1782],{"style":1778},"top:-3em;",[568,1780],{"className":1781,"style":1351},[1295],[568,1783,1785],{"className":1784},[628],[568,1786,589],{"className":1787,"style":630},[628,629],[568,1789,1791,1794],{"style":1790},"top:-3.5506em;",[568,1792],{"className":1793,"style":1351},[1295],[568,1795],{"className":1796,"style":1375},[1797],"overline-line"," mit der konjugiert komplexen Zahl ",[568,1800,1802,1831],{"className":1801},[571],[568,1803,1805],{"className":1804},[575],[577,1806,1807],{"xmlns":579},[581,1808,1809,1828],{},[584,1810,1811,1817,1819,1821,1824,1826],{},[1669,1812,1813,1815],{"accent":615},[587,1814,589],{},[591,1816,1675],{"stretchy":615},[591,1818,593],{},[587,1820,596],{},[591,1822,1823],{},"−",[587,1825,602],{},[587,1827,605],{},[607,1829,1830],{"encoding":609},"\\overline{z} = a - bi",[568,1832,1834,1880,1898],{"className":1833,"ariaHidden":615},[614],[568,1835,1837,1840,1871,1874,1877],{"className":1836},[619],[568,1838],{"className":1839,"style":1762},[623],[568,1841,1843],{"className":1842},[628,1766],[568,1844,1846],{"className":1845},[1278],[568,1847,1849],{"className":1848},[1283],[568,1850,1852,1863],{"className":1851,"style":1762},[1287],[568,1853,1854,1857],{"style":1778},[568,1855],{"className":1856,"style":1351},[1295],[568,1858,1860],{"className":1859},[628],[568,1861,589],{"className":1862,"style":630},[628,629],[568,1864,1865,1868],{"style":1790},[568,1866],{"className":1867,"style":1351},[1295],[568,1869],{"className":1870,"style":1375},[1797],[568,1872],{"className":1873,"style":635},[634],[568,1875,593],{"className":1876},[639],[568,1878],{"className":1879,"style":635},[634],[568,1881,1883,1886,1889,1892,1895],{"className":1882},[619],[568,1884],{"className":1885,"style":649},[623],[568,1887,596],{"className":1888},[628,629],[568,1890],{"className":1891,"style":656},[634],[568,1893,1823],{"className":1894},[660],[568,1896],{"className":1897,"style":656},[634],[568,1899,1901,1904],{"className":1900},[619],[568,1902],{"className":1903,"style":670},[623],[568,1905,674],{"className":1906},[628,629],[798,1908,1909,1970,1971,1204,1999,2027],{},[568,1910,1912,1934],{"className":1911},[571],[568,1913,1915],{"className":1914},[575],[577,1916,1917],{"xmlns":579},[581,1918,1919,1931],{},[584,1920,1921,1923,1925,1927,1929],{},[587,1922,696],{"mathvariant":764},[587,1924,589],{},[591,1926,1823],{},[587,1928,1097],{},[587,1930,696],{"mathvariant":764},[607,1932,1933],{"encoding":609},"|z - w|",[568,1935,1937,1958],{"className":1936,"ariaHidden":615},[614],[568,1938,1940,1943,1946,1949,1952,1955],{"className":1939},[619],[568,1941],{"className":1942,"style":714},[623],[568,1944,696],{"className":1945},[628],[568,1947,589],{"className":1948,"style":630},[628,629],[568,1950],{"className":1951,"style":656},[634],[568,1953,1823],{"className":1954},[660],[568,1956],{"className":1957,"style":656},[634],[568,1959,1961,1964,1967],{"className":1960},[619],[568,1962],{"className":1963,"style":714},[623],[568,1965,1097],{"className":1966,"style":1152},[628,629],[568,1968,696],{"className":1969},[628]," ist der Abstand der Punkte ",[568,1972,1974,1987],{"className":1973},[571],[568,1975,1977],{"className":1976},[575],[577,1978,1979],{"xmlns":579},[581,1980,1981,1985],{},[584,1982,1983],{},[587,1984,589],{},[607,1986,589],{"encoding":609},[568,1988,1990],{"className":1989,"ariaHidden":615},[614],[568,1991,1993,1996],{"className":1992},[619],[568,1994],{"className":1995,"style":624},[623],[568,1997,589],{"className":1998,"style":630},[628,629],[568,2000,2002,2015],{"className":2001},[571],[568,2003,2005],{"className":2004},[575],[577,2006,2007],{"xmlns":579},[581,2008,2009,2013],{},[584,2010,2011],{},[587,2012,1097],{},[607,2014,1097],{"encoding":609},[568,2016,2018],{"className":2017,"ariaHidden":615},[614],[568,2019,2021,2024],{"className":2020},[619],[568,2022],{"className":2023,"style":624},[623],[568,2025,1097],{"className":2026,"style":1152},[628,629]," in der Zahlenebene.",[559,2029,2031],{"id":2030},"beispiele","Beispiele",[568,2033,2036],{"className":2034},[2035],"katex-display",[568,2037,2039,2099],{"className":2038},[571],[568,2040,2042],{"className":2041},[575],[577,2043,2045],{"xmlns":579,"display":2044},"block",[581,2046,2047,2096],{},[584,2048,2049,2051,2054,2056,2059,2061,2063,2065,2084,2086,2091,2093],{},[587,2050,696],{"mathvariant":764},[822,2052,2053],{},"3",[591,2055,599],{},[822,2057,2058],{},"4",[587,2060,605],{},[587,2062,696],{"mathvariant":764},[591,2064,593],{},[2066,2067,2068],"msqrt",{},[584,2069,2070,2076,2078],{},[1655,2071,2072,2074],{},[822,2073,2053],{},[822,2075,1661],{},[591,2077,599],{},[1655,2079,2080,2082],{},[822,2081,2058],{},[822,2083,1661],{},[591,2085,593],{},[2066,2087,2088],{},[822,2089,2090],{},"25",[591,2092,593],{},[822,2094,2095],{},"5",[607,2097,2098],{"encoding":609},"|3 + 4i| = \\sqrt{3^2 + 4^2} = \\sqrt{25} = 5",[568,2100,2102,2121,2145,2288,2359],{"className":2101,"ariaHidden":615},[614],[568,2103,2105,2108,2112,2115,2118],{"className":2104},[619],[568,2106],{"className":2107,"style":714},[623],[568,2109,2111],{"className":2110},[628],"∣3",[568,2113],{"className":2114,"style":656},[634],[568,2116,599],{"className":2117},[660],[568,2119],{"className":2120,"style":656},[634],[568,2122,2124,2127,2130,2133,2136,2139,2142],{"className":2123},[619],[568,2125],{"className":2126,"style":714},[623],[568,2128,2058],{"className":2129},[628],[568,2131,605],{"className":2132},[628,629],[568,2134,696],{"className":2135},[628],[568,2137],{"className":2138,"style":635},[634],[568,2140,593],{"className":2141},[639],[568,2143],{"className":2144,"style":635},[634],[568,2146,2148,2152,2279,2282,2285],{"className":2147},[619],[568,2149],{"className":2150,"style":2151},[623],"height:1.24em;vertical-align:-0.1777em;",[568,2153,2156],{"className":2154},[628,2155],"sqrt",[568,2157,2159,2270],{"className":2158},[1278,1279],[568,2160,2162,2267],{"className":2161},[1283],[568,2163,2166,2247],{"className":2164,"style":2165},[1287],"height:1.0623em;",[568,2167,2171,2174],{"className":2168,"style":2170},[2169],"svg-align","top:-3.2em;",[568,2172],{"className":2173,"style":1296},[1295],[568,2175,2178,2209,2212,2215,2218],{"className":2176,"style":2177},[628],"padding-left:1em;",[568,2179,2181,2184],{"className":2180},[628],[568,2182,2053],{"className":2183},[628],[568,2185,2187],{"className":2186},[1704],[568,2188,2190],{"className":2189},[1278],[568,2191,2193],{"className":2192},[1283],[568,2194,2197],{"className":2195,"style":2196},[1287],"height:0.7401em;",[568,2198,2200,2203],{"style":2199},"top:-2.989em;margin-right:0.05em;",[568,2201],{"className":2202,"style":1721},[1295],[568,2204,2206],{"className":2205},[1355,1356,1357,1358],[568,2207,1661],{"className":2208},[628,1358],[568,2210],{"className":2211,"style":656},[634],[568,2213,599],{"className":2214},[660],[568,2216],{"className":2217,"style":656},[634],[568,2219,2221,2224],{"className":2220},[628],[568,2222,2058],{"className":2223},[628],[568,2225,2227],{"className":2226},[1704],[568,2228,2230],{"className":2229},[1278],[568,2231,2233],{"className":2232},[1283],[568,2234,2236],{"className":2235,"style":2196},[1287],[568,2237,2238,2241],{"style":2199},[568,2239],{"className":2240,"style":1721},[1295],[568,2242,2244],{"className":2243},[1355,1356,1357,1358],[568,2245,1661],{"className":2246},[628,1358],[568,2248,2250,2253],{"style":2249},"top:-3.0223em;",[568,2251],{"className":2252,"style":1296},[1295],[568,2254,2258],{"className":2255,"style":2257},[2256],"hide-tail","min-width:1.02em;height:1.28em;",[1301,2259,2264],{"xmlns":1303,"width":2260,"height":2261,"viewBox":2262,"preserveAspectRatio":2263},"400em","1.28em","0 0 400000 1296","xMinYMin slice",[1308,2265],{"d":2266},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[568,2268,1315],{"className":2269},[1314],[568,2271,2273],{"className":2272},[1283],[568,2274,2277],{"className":2275,"style":2276},[1287],"height:0.1777em;",[568,2278],{},[568,2280],{"className":2281,"style":635},[634],[568,2283,593],{"className":2284},[639],[568,2286],{"className":2287,"style":635},[634],[568,2289,2291,2295,2350,2353,2356],{"className":2290},[619],[568,2292],{"className":2293,"style":2294},[623],"height:1.04em;vertical-align:-0.0839em;",[568,2296,2298],{"className":2297},[628,2155],[568,2299,2301,2341],{"className":2300},[1278,1279],[568,2302,2304,2338],{"className":2303},[1283],[568,2305,2308,2321],{"className":2306,"style":2307},[1287],"height:0.9561em;",[568,2309,2311,2314],{"className":2310,"style":1778},[2169],[568,2312],{"className":2313,"style":1351},[1295],[568,2315,2318],{"className":2316,"style":2317},[628],"padding-left:0.833em;",[568,2319,2090],{"className":2320},[628],[568,2322,2324,2327],{"style":2323},"top:-2.9161em;",[568,2325],{"className":2326,"style":1351},[1295],[568,2328,2331],{"className":2329,"style":2330},[2256],"min-width:0.853em;height:1.08em;",[1301,2332,2335],{"xmlns":1303,"width":2260,"height":2333,"viewBox":2334,"preserveAspectRatio":2263},"1.08em","0 0 400000 1080",[1308,2336],{"d":2337},"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",[568,2339,1315],{"className":2340},[1314],[568,2342,2344],{"className":2343},[1283],[568,2345,2348],{"className":2346,"style":2347},[1287],"height:0.0839em;",[568,2349],{},[568,2351],{"className":2352,"style":635},[634],[568,2354,593],{"className":2355},[639],[568,2357],{"className":2358,"style":635},[634],[568,2360,2362,2365],{"className":2361},[619],[568,2363],{"className":2364,"style":861},[623],[568,2366,2095],{"className":2367},[628],[568,2369,2371],{"className":2370},[2035],[568,2372,2374,2455],{"className":2373},[571],[568,2375,2377],{"className":2376},[575],[577,2378,2379],{"xmlns":579,"display":2044},[581,2380,2381,2452],{},[584,2382,2383,2385,2387,2389,2391,2393,2395,2397,2422,2424,2428,2431,2434,2437,2440,2442,2444,2446,2448,2450],{},[587,2384,696],{"mathvariant":764},[591,2386,1823],{},[822,2388,1661],{},[591,2390,599],{},[587,2392,605],{},[587,2394,696],{"mathvariant":764},[591,2396,593],{},[2066,2398,2399],{},[584,2400,2401,2403,2405,2407,2413,2415],{},[591,2402,691],{"stretchy":690},[591,2404,1823],{},[822,2406,1661],{},[1655,2408,2409,2411],{},[591,2410,701],{"stretchy":690},[822,2412,1661],{},[591,2414,599],{},[1655,2416,2417,2420],{},[822,2418,2419],{},"1",[822,2421,1661],{},[591,2423,593],{},[2066,2425,2426],{},[822,2427,2095],{},[591,2429,2430],{},"≈",[822,2432,2433],{},"2,2361",[591,2435,2436],{"separator":615},",",[634,2438],{"width":2439},"2em",[587,2441,696],{"mathvariant":764},[822,2443,1661],{},[587,2445,605],{},[587,2447,696],{"mathvariant":764},[591,2449,593],{},[822,2451,1661],{},[607,2453,2454],{"encoding":609},"|-2 + i| = \\sqrt{(-2)^2 + 1^2} = \\sqrt{5} \\approx 2{,}2361, \\qquad |2i| = 2",[568,2456,2458,2476,2495,2516,2655,2717,2767],{"className":2457,"ariaHidden":615},[614],[568,2459,2461,2464,2467,2470,2473],{"className":2460},[619],[568,2462],{"className":2463,"style":714},[623],[568,2465,696],{"className":2466},[628],[568,2468],{"className":2469,"style":656},[634],[568,2471,1823],{"className":2472},[660],[568,2474],{"className":2475,"style":656},[634],[568,2477,2479,2483,2486,2489,2492],{"className":2478},[619],[568,2480],{"className":2481,"style":2482},[623],"height:0.7278em;vertical-align:-0.0833em;",[568,2484,1661],{"className":2485},[628],[568,2487],{"className":2488,"style":656},[634],[568,2490,599],{"className":2491},[660],[568,2493],{"className":2494,"style":656},[634],[568,2496,2498,2501,2504,2507,2510,2513],{"className":2497},[619],[568,2499],{"className":2500,"style":714},[623],[568,2502,605],{"className":2503},[628,629],[568,2505,696],{"className":2506},[628],[568,2508],{"className":2509,"style":635},[634],[568,2511,593],{"className":2512},[639],[568,2514],{"className":2515,"style":635},[634],[568,2517,2519,2523,2646,2649,2652],{"className":2518},[619],[568,2520],{"className":2521,"style":2522},[623],"height:1.24em;vertical-align:-0.2561em;",[568,2524,2526],{"className":2525},[628,2155],[568,2527,2529,2637],{"className":2528},[1278,1279],[568,2530,2532,2634],{"className":2531},[1283],[568,2533,2536,2621],{"className":2534,"style":2535},[1287],"height:0.9839em;",[568,2537,2539,2542],{"className":2538,"style":2170},[2169],[568,2540],{"className":2541,"style":1296},[1295],[568,2543,2545,2548,2551,2554,2583,2586,2589,2592],{"className":2544,"style":2177},[628],[568,2546,691],{"className":2547},[718],[568,2549,1823],{"className":2550},[628],[568,2552,1661],{"className":2553},[628],[568,2555,2557,2560],{"className":2556},[743],[568,2558,701],{"className":2559},[743],[568,2561,2563],{"className":2562},[1704],[568,2564,2566],{"className":2565},[1278],[568,2567,2569],{"className":2568},[1283],[568,2570,2572],{"className":2571,"style":2196},[1287],[568,2573,2574,2577],{"style":2199},[568,2575],{"className":2576,"style":1721},[1295],[568,2578,2580],{"className":2579},[1355,1356,1357,1358],[568,2581,1661],{"className":2582},[628,1358],[568,2584],{"className":2585,"style":656},[634],[568,2587,599],{"className":2588},[660],[568,2590],{"className":2591,"style":656},[634],[568,2593,2595,2598],{"className":2594},[628],[568,2596,2419],{"className":2597},[628],[568,2599,2601],{"className":2600},[1704],[568,2602,2604],{"className":2603},[1278],[568,2605,2607],{"className":2606},[1283],[568,2608,2610],{"className":2609,"style":2196},[1287],[568,2611,2612,2615],{"style":2199},[568,2613],{"className":2614,"style":1721},[1295],[568,2616,2618],{"className":2617},[1355,1356,1357,1358],[568,2619,1661],{"className":2620},[628,1358],[568,2622,2624,2627],{"style":2623},"top:-2.9439em;",[568,2625],{"className":2626,"style":1296},[1295],[568,2628,2630],{"className":2629,"style":2257},[2256],[1301,2631,2632],{"xmlns":1303,"width":2260,"height":2261,"viewBox":2262,"preserveAspectRatio":2263},[1308,2633],{"d":2266},[568,2635,1315],{"className":2636},[1314],[568,2638,2640],{"className":2639},[1283],[568,2641,2644],{"className":2642,"style":2643},[1287],"height:0.2561em;",[568,2645],{},[568,2647],{"className":2648,"style":635},[634],[568,2650,593],{"className":2651},[639],[568,2653],{"className":2654,"style":635},[634],[568,2656,2658,2661,2708,2711,2714],{"className":2657},[619],[568,2659],{"className":2660,"style":2294},[623],[568,2662,2664],{"className":2663},[628,2155],[568,2665,2667,2700],{"className":2666},[1278,1279],[568,2668,2670,2697],{"className":2669},[1283],[568,2671,2673,2685],{"className":2672,"style":2307},[1287],[568,2674,2676,2679],{"className":2675,"style":1778},[2169],[568,2677],{"className":2678,"style":1351},[1295],[568,2680,2682],{"className":2681,"style":2317},[628],[568,2683,2095],{"className":2684},[628],[568,2686,2687,2690],{"style":2323},[568,2688],{"className":2689,"style":1351},[1295],[568,2691,2693],{"className":2692,"style":2330},[2256],[1301,2694,2695],{"xmlns":1303,"width":2260,"height":2333,"viewBox":2334,"preserveAspectRatio":2263},[1308,2696],{"d":2337},[568,2698,1315],{"className":2699},[1314],[568,2701,2703],{"className":2702},[1283],[568,2704,2706],{"className":2705,"style":2347},[1287],[568,2707],{},[568,2709],{"className":2710,"style":635},[634],[568,2712,2430],{"className":2713},[639],[568,2715],{"className":2716,"style":635},[634],[568,2718,2720,2723,2726,2733,2737,2740,2744,2748,2752,2755,2758,2761,2764],{"className":2719},[619],[568,2721],{"className":2722,"style":714},[623],[568,2724,1661],{"className":2725},[628],[568,2727,2729],{"className":2728},[628],[568,2730,2436],{"className":2731},[2732],"mpunct",[568,2734,2736],{"className":2735},[628],"2361",[568,2738,2436],{"className":2739},[2732],[568,2741],{"className":2742,"style":2743},[634],"margin-right:2em;",[568,2745],{"className":2746,"style":2747},[634],"margin-right:0.1667em;",[568,2749,2751],{"className":2750},[628],"∣2",[568,2753,605],{"className":2754},[628,629],[568,2756,696],{"className":2757},[628],[568,2759],{"className":2760,"style":635},[634],[568,2762,593],{"className":2763},[639],[568,2765],{"className":2766,"style":635},[634],[568,2768,2770,2773],{"className":2769},[619],[568,2771],{"className":2772,"style":861},[623],[568,2774,1661],{"className":2775},[628],[564,2777,2778,2779,1204,2831,2887],{},"Abstand von ",[568,2780,2782,2800],{"className":2781},[571],[568,2783,2785],{"className":2784},[575],[577,2786,2787],{"xmlns":579},[581,2788,2789,2797],{},[584,2790,2791,2793,2795],{},[822,2792,2419],{},[591,2794,599],{},[587,2796,605],{},[607,2798,2799],{"encoding":609},"1 + i",[568,2801,2803,2821],{"className":2802,"ariaHidden":615},[614],[568,2804,2806,2809,2812,2815,2818],{"className":2805},[619],[568,2807],{"className":2808,"style":2482},[623],[568,2810,2419],{"className":2811},[628],[568,2813],{"className":2814,"style":656},[634],[568,2816,599],{"className":2817},[660],[568,2819],{"className":2820,"style":656},[634],[568,2822,2824,2828],{"className":2823},[619],[568,2825],{"className":2826,"style":2827},[623],"height:0.6595em;",[568,2829,605],{"className":2830},[628,629],[568,2832,2834,2854],{"className":2833},[571],[568,2835,2837],{"className":2836},[575],[577,2838,2839],{"xmlns":579},[581,2840,2841,2851],{},[584,2842,2843,2845,2847,2849],{},[822,2844,2058],{},[591,2846,599],{},[822,2848,2095],{},[587,2850,605],{},[607,2852,2853],{"encoding":609},"4 + 5i",[568,2855,2857,2875],{"className":2856,"ariaHidden":615},[614],[568,2858,2860,2863,2866,2869,2872],{"className":2859},[619],[568,2861],{"className":2862,"style":2482},[623],[568,2864,2058],{"className":2865},[628],[568,2867],{"className":2868,"style":656},[634],[568,2870,599],{"className":2871},[660],[568,2873],{"className":2874,"style":656},[634],[568,2876,2878,2881,2884],{"className":2877},[619],[568,2879],{"className":2880,"style":2827},[623],[568,2882,2095],{"className":2883},[628],[568,2885,605],{"className":2886},[628,629],":",[568,2889,2891],{"className":2890},[2035],[568,2892,2894,2952],{"className":2893},[571],[568,2895,2897],{"className":2896},[575],[577,2898,2899],{"xmlns":579,"display":2044},[581,2900,2901,2949],{},[584,2902,2903,2905,2907,2909,2911,2913,2915,2917,2919,2921,2923,2925,2927,2929,2931,2933,2935,2937,2939,2941,2943,2945,2947],{},[587,2904,696],{"mathvariant":764},[591,2906,691],{"stretchy":690},[822,2908,2058],{},[591,2910,599],{},[822,2912,2095],{},[587,2914,605],{},[591,2916,701],{"stretchy":690},[591,2918,1823],{},[591,2920,691],{"stretchy":690},[822,2922,2419],{},[591,2924,599],{},[587,2926,605],{},[591,2928,701],{"stretchy":690},[587,2930,696],{"mathvariant":764},[591,2932,593],{},[587,2934,696],{"mathvariant":764},[822,2936,2053],{},[591,2938,599],{},[822,2940,2058],{},[587,2942,605],{},[587,2944,696],{"mathvariant":764},[591,2946,593],{},[822,2948,2095],{},[607,2950,2951],{"encoding":609},"|(4 + 5i) - (1 + i)| = |3 + 4i| = 5",[568,2953,2955,2979,3003,3024,3048,3066,3090],{"className":2954,"ariaHidden":615},[614],[568,2956,2958,2961,2964,2967,2970,2973,2976],{"className":2957},[619],[568,2959],{"className":2960,"style":714},[623],[568,2962,696],{"className":2963},[628],[568,2965,691],{"className":2966},[718],[568,2968,2058],{"className":2969},[628],[568,2971],{"className":2972,"style":656},[634],[568,2974,599],{"className":2975},[660],[568,2977],{"className":2978,"style":656},[634],[568,2980,2982,2985,2988,2991,2994,2997,3000],{"className":2981},[619],[568,2983],{"className":2984,"style":714},[623],[568,2986,2095],{"className":2987},[628],[568,2989,605],{"className":2990},[628,629],[568,2992,701],{"className":2993},[743],[568,2995],{"className":2996,"style":656},[634],[568,2998,1823],{"className":2999},[660],[568,3001],{"className":3002,"style":656},[634],[568,3004,3006,3009,3012,3015,3018,3021],{"className":3005},[619],[568,3007],{"className":3008,"style":714},[623],[568,3010,691],{"className":3011},[718],[568,3013,2419],{"className":3014},[628],[568,3016],{"className":3017,"style":656},[634],[568,3019,599],{"className":3020},[660],[568,3022],{"className":3023,"style":656},[634],[568,3025,3027,3030,3033,3036,3039,3042,3045],{"className":3026},[619],[568,3028],{"className":3029,"style":714},[623],[568,3031,605],{"className":3032},[628,629],[568,3034,701],{"className":3035},[743],[568,3037,696],{"className":3038},[628],[568,3040],{"className":3041,"style":635},[634],[568,3043,593],{"className":3044},[639],[568,3046],{"className":3047,"style":635},[634],[568,3049,3051,3054,3057,3060,3063],{"className":3050},[619],[568,3052],{"className":3053,"style":714},[623],[568,3055,2111],{"className":3056},[628],[568,3058],{"className":3059,"style":656},[634],[568,3061,599],{"className":3062},[660],[568,3064],{"className":3065,"style":656},[634],[568,3067,3069,3072,3075,3078,3081,3084,3087],{"className":3068},[619],[568,3070],{"className":3071,"style":714},[623],[568,3073,2058],{"className":3074},[628],[568,3076,605],{"className":3077},[628,629],[568,3079,696],{"className":3080},[628],[568,3082],{"className":3083,"style":635},[634],[568,3085,593],{"className":3086},[639],[568,3088],{"className":3089,"style":635},[634],[568,3091,3093,3096],{"className":3092},[619],[568,3094],{"className":3095,"style":861},[623],[568,3097,2095],{"className":3098},[628],[564,3100,3101],{},"Betrag eines Produkts ohne Ausmultiplizieren:",[568,3103,3105],{"className":3104},[2035],[568,3106,3108,3182],{"className":3107},[571],[568,3109,3111],{"className":3110},[575],[577,3112,3113],{"xmlns":579,"display":2044},[581,3114,3115,3179],{},[584,3116,3117,3119,3121,3123,3125,3127,3129,3131,3133,3135,3137,3139,3141,3143,3145,3147,3149,3151,3153,3155,3157,3159,3161,3163,3165,3167,3169,3171,3175,3177],{},[587,3118,696],{"mathvariant":764},[591,3120,691],{"stretchy":690},[822,3122,2419],{},[591,3124,599],{},[587,3126,605],{},[591,3128,701],{"stretchy":690},[591,3130,691],{"stretchy":690},[822,3132,2053],{},[591,3134,599],{},[822,3136,2058],{},[587,3138,605],{},[591,3140,701],{"stretchy":690},[587,3142,696],{"mathvariant":764},[591,3144,593],{},[587,3146,696],{"mathvariant":764},[822,3148,2419],{},[591,3150,599],{},[587,3152,605],{},[587,3154,696],{"mathvariant":764},[591,3156,1094],{},[587,3158,696],{"mathvariant":764},[822,3160,2053],{},[591,3162,599],{},[822,3164,2058],{},[587,3166,605],{},[587,3168,696],{"mathvariant":764},[591,3170,593],{},[2066,3172,3173],{},[822,3174,1661],{},[591,3176,1094],{},[822,3178,2095],{},[607,3180,3181],{"encoding":609},"|(1 + i)(3 + 4i)| = |1 + i| \\cdot |3 + 4i| = \\sqrt{2} \\cdot 5",[568,3183,3185,3209,3236,3263,3282,3303,3321,3345,3407],{"className":3184,"ariaHidden":615},[614],[568,3186,3188,3191,3194,3197,3200,3203,3206],{"className":3187},[619],[568,3189],{"className":3190,"style":714},[623],[568,3192,696],{"className":3193},[628],[568,3195,691],{"className":3196},[718],[568,3198,2419],{"className":3199},[628],[568,3201],{"className":3202,"style":656},[634],[568,3204,599],{"className":3205},[660],[568,3207],{"className":3208,"style":656},[634],[568,3210,3212,3215,3218,3221,3224,3227,3230,3233],{"className":3211},[619],[568,3213],{"className":3214,"style":714},[623],[568,3216,605],{"className":3217},[628,629],[568,3219,701],{"className":3220},[743],[568,3222,691],{"className":3223},[718],[568,3225,2053],{"className":3226},[628],[568,3228],{"className":3229,"style":656},[634],[568,3231,599],{"className":3232},[660],[568,3234],{"className":3235,"style":656},[634],[568,3237,3239,3242,3245,3248,3251,3254,3257,3260],{"className":3238},[619],[568,3240],{"className":3241,"style":714},[623],[568,3243,2058],{"className":3244},[628],[568,3246,605],{"className":3247},[628,629],[568,3249,701],{"className":3250},[743],[568,3252,696],{"className":3253},[628],[568,3255],{"className":3256,"style":635},[634],[568,3258,593],{"className":3259},[639],[568,3261],{"className":3262,"style":635},[634],[568,3264,3266,3269,3273,3276,3279],{"className":3265},[619],[568,3267],{"className":3268,"style":714},[623],[568,3270,3272],{"className":3271},[628],"∣1",[568,3274],{"className":3275,"style":656},[634],[568,3277,599],{"className":3278},[660],[568,3280],{"className":3281,"style":656},[634],[568,3283,3285,3288,3291,3294,3297,3300],{"className":3284},[619],[568,3286],{"className":3287,"style":714},[623],[568,3289,605],{"className":3290},[628,629],[568,3292,696],{"className":3293},[628],[568,3295],{"className":3296,"style":656},[634],[568,3298,1094],{"className":3299},[660],[568,3301],{"className":3302,"style":656},[634],[568,3304,3306,3309,3312,3315,3318],{"className":3305},[619],[568,3307],{"className":3308,"style":714},[623],[568,3310,2111],{"className":3311},[628],[568,3313],{"className":3314,"style":656},[634],[568,3316,599],{"className":3317},[660],[568,3319],{"className":3320,"style":656},[634],[568,3322,3324,3327,3330,3333,3336,3339,3342],{"className":3323},[619],[568,3325],{"className":3326,"style":714},[623],[568,3328,2058],{"className":3329},[628],[568,3331,605],{"className":3332},[628,629],[568,3334,696],{"className":3335},[628],[568,3337],{"className":3338,"style":635},[634],[568,3340,593],{"className":3341},[639],[568,3343],{"className":3344,"style":635},[634],[568,3346,3348,3351,3398,3401,3404],{"className":3347},[619],[568,3349],{"className":3350,"style":2294},[623],[568,3352,3354],{"className":3353},[628,2155],[568,3355,3357,3390],{"className":3356},[1278,1279],[568,3358,3360,3387],{"className":3359},[1283],[568,3361,3363,3375],{"className":3362,"style":2307},[1287],[568,3364,3366,3369],{"className":3365,"style":1778},[2169],[568,3367],{"className":3368,"style":1351},[1295],[568,3370,3372],{"className":3371,"style":2317},[628],[568,3373,1661],{"className":3374},[628],[568,3376,3377,3380],{"style":2323},[568,3378],{"className":3379,"style":1351},[1295],[568,3381,3383],{"className":3382,"style":2330},[2256],[1301,3384,3385],{"xmlns":1303,"width":2260,"height":2333,"viewBox":2334,"preserveAspectRatio":2263},[1308,3386],{"d":2337},[568,3388,1315],{"className":3389},[1314],[568,3391,3393],{"className":3392},[1283],[568,3394,3396],{"className":3395,"style":2347},[1287],[568,3397],{},[568,3399],{"className":3400,"style":656},[634],[568,3402,1094],{"className":3403},[660],[568,3405],{"className":3406,"style":656},[634],[568,3408,3410,3413],{"className":3409},[619],[568,3411],{"className":3412,"style":861},[623],[568,3414,2095],{"className":3415},[628],[559,3417,3419],{"id":3418},"typische-fehler","Typische Fehler",[795,3421,3422,3799,3975],{},[798,3423,3424,3425,3453,3454,3718,3719,3770,3771,979],{},"Das ",[568,3426,3428,3441],{"className":3427},[571],[568,3429,3431],{"className":3430},[575],[577,3432,3433],{"xmlns":579},[581,3434,3435,3439],{},[584,3436,3437],{},[587,3438,605],{},[607,3440,605],{"encoding":609},[568,3442,3444],{"className":3443,"ariaHidden":615},[614],[568,3445,3447,3450],{"className":3446},[619],[568,3448],{"className":3449,"style":2827},[623],[568,3451,605],{"className":3452},[628,629]," mitquadrieren: ",[568,3455,3457,3507],{"className":3456},[571],[568,3458,3460],{"className":3459},[575],[577,3461,3462],{"xmlns":579},[581,3463,3464,3504],{},[584,3465,3466,3490,3492],{},[2066,3467,3468],{},[584,3469,3470,3476,3478,3480,3482,3484],{},[1655,3471,3472,3474],{},[822,3473,2053],{},[822,3475,1661],{},[591,3477,599],{},[591,3479,691],{"stretchy":690},[822,3481,2058],{},[587,3483,605],{},[1655,3485,3486,3488],{},[591,3487,701],{"stretchy":690},[822,3489,1661],{},[591,3491,593],{},[2066,3493,3494],{},[584,3495,3496,3499,3501],{},[822,3497,3498],{},"9",[591,3500,1823],{},[822,3502,3503],{},"16",[607,3505,3506],{"encoding":609},"\\sqrt{3^2 + (4i)^2} = \\sqrt{9 - 16}",[568,3508,3510,3649],{"className":3509,"ariaHidden":615},[614],[568,3511,3513,3517,3640,3643,3646],{"className":3512},[619],[568,3514],{"className":3515,"style":3516},[623],"height:1.24em;vertical-align:-0.305em;",[568,3518,3520],{"className":3519},[628,2155],[568,3521,3523,3631],{"className":3522},[1278,1279],[568,3524,3526,3628],{"className":3525},[1283],[568,3527,3530,3615],{"className":3528,"style":3529},[1287],"height:0.935em;",[568,3531,3533,3536],{"className":3532,"style":2170},[2169],[568,3534],{"className":3535,"style":1296},[1295],[568,3537,3539,3568,3571,3574,3577,3580,3583,3586],{"className":3538,"style":2177},[628],[568,3540,3542,3545],{"className":3541},[628],[568,3543,2053],{"className":3544},[628],[568,3546,3548],{"className":3547},[1704],[568,3549,3551],{"className":3550},[1278],[568,3552,3554],{"className":3553},[1283],[568,3555,3557],{"className":3556,"style":2196},[1287],[568,3558,3559,3562],{"style":2199},[568,3560],{"className":3561,"style":1721},[1295],[568,3563,3565],{"className":3564},[1355,1356,1357,1358],[568,3566,1661],{"className":3567},[628,1358],[568,3569],{"className":3570,"style":656},[634],[568,3572,599],{"className":3573},[660],[568,3575],{"className":3576,"style":656},[634],[568,3578,691],{"className":3579},[718],[568,3581,2058],{"className":3582},[628],[568,3584,605],{"className":3585},[628,629],[568,3587,3589,3592],{"className":3588},[743],[568,3590,701],{"className":3591},[743],[568,3593,3595],{"className":3594},[1704],[568,3596,3598],{"className":3597},[1278],[568,3599,3601],{"className":3600},[1283],[568,3602,3604],{"className":3603,"style":2196},[1287],[568,3605,3606,3609],{"style":2199},[568,3607],{"className":3608,"style":1721},[1295],[568,3610,3612],{"className":3611},[1355,1356,1357,1358],[568,3613,1661],{"className":3614},[628,1358],[568,3616,3618,3621],{"style":3617},"top:-2.895em;",[568,3619],{"className":3620,"style":1296},[1295],[568,3622,3624],{"className":3623,"style":2257},[2256],[1301,3625,3626],{"xmlns":1303,"width":2260,"height":2261,"viewBox":2262,"preserveAspectRatio":2263},[1308,3627],{"d":2266},[568,3629,1315],{"className":3630},[1314],[568,3632,3634],{"className":3633},[1283],[568,3635,3638],{"className":3636,"style":3637},[1287],"height:0.305em;",[568,3639],{},[568,3641],{"className":3642,"style":635},[634],[568,3644,593],{"className":3645},[639],[568,3647],{"className":3648,"style":635},[634],[568,3650,3652,3656],{"className":3651},[619],[568,3653],{"className":3654,"style":3655},[623],"height:1.04em;vertical-align:-0.1744em;",[568,3657,3659],{"className":3658},[628,2155],[568,3660,3662,3709],{"className":3661},[1278,1279],[568,3663,3665,3706],{"className":3664},[1283],[568,3666,3669,3693],{"className":3667,"style":3668},[1287],"height:0.8656em;",[568,3670,3672,3675],{"className":3671,"style":1778},[2169],[568,3673],{"className":3674,"style":1351},[1295],[568,3676,3678,3681,3684,3687,3690],{"className":3677,"style":2317},[628],[568,3679,3498],{"className":3680},[628],[568,3682],{"className":3683,"style":656},[634],[568,3685,1823],{"className":3686},[660],[568,3688],{"className":3689,"style":656},[634],[568,3691,3503],{"className":3692},[628],[568,3694,3696,3699],{"style":3695},"top:-2.8256em;",[568,3697],{"className":3698,"style":1351},[1295],[568,3700,3702],{"className":3701,"style":2330},[2256],[1301,3703,3704],{"xmlns":1303,"width":2260,"height":2333,"viewBox":2334,"preserveAspectRatio":2263},[1308,3705],{"d":2337},[568,3707,1315],{"className":3708},[1314],[568,3710,3712],{"className":3711},[1283],[568,3713,3716],{"className":3714,"style":3715},[1287],"height:0.1744em;",[568,3717],{}," ist falsch. In die Formel kommt der Imaginärteil ",[568,3720,3722,3740],{"className":3721},[571],[568,3723,3725],{"className":3724},[575],[577,3726,3727],{"xmlns":579},[581,3728,3729,3737],{},[584,3730,3731,3733,3735],{},[587,3732,602],{},[591,3734,593],{},[822,3736,2058],{},[607,3738,3739],{"encoding":609},"b = 4",[568,3741,3743,3761],{"className":3742,"ariaHidden":615},[614],[568,3744,3746,3749,3752,3755,3758],{"className":3745},[619],[568,3747],{"className":3748,"style":670},[623],[568,3750,602],{"className":3751},[628,629],[568,3753],{"className":3754,"style":635},[634],[568,3756,593],{"className":3757},[639],[568,3759],{"className":3760,"style":635},[634],[568,3762,3764,3767],{"className":3763},[619],[568,3765],{"className":3766,"style":861},[623],[568,3768,2058],{"className":3769},[628]," ohne ",[568,3772,3774,3787],{"className":3773},[571],[568,3775,3777],{"className":3776},[575],[577,3778,3779],{"xmlns":579},[581,3780,3781,3785],{},[584,3782,3783],{},[587,3784,605],{},[607,3786,605],{"encoding":609},[568,3788,3790],{"className":3789,"ariaHidden":615},[614],[568,3791,3793,3796],{"className":3792},[619],[568,3794],{"className":3795,"style":2827},[623],[568,3797,605],{"className":3798},[628,629],[798,3800,3801,3802,979],{},"Real- und Imaginärteil einfach addieren: 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7",[568,3851,3853,3871,3928,3947,3966],{"className":3852,"ariaHidden":615},[614],[568,3854,3856,3859,3862,3865,3868],{"className":3855},[619],[568,3857],{"className":3858,"style":714},[623],[568,3860,2111],{"className":3861},[628],[568,3863],{"className":3864,"style":656},[634],[568,3866,599],{"className":3867},[660],[568,3869],{"className":3870,"style":656},[634],[568,3872,3874,3877,3880,3883,3886,3889,3925],{"className":3873},[619],[568,3875],{"className":3876,"style":714},[623],[568,3878,2058],{"className":3879},[628],[568,3881,605],{"className":3882},[628,629],[568,3884,696],{"className":3885},[628],[568,3887],{"className":3888,"style":635},[634],[568,3890,3892,3919,3922],{"className":3891},[639],[568,3893,3895],{"className":3894},[639],[568,3896,3898],{"className":3897},[628,1590],[568,3899,3901],{"className":3900},[1594],[568,3902,3904,3907,3916],{"className":3903},[1598],[568,3905],{"className":3906,"style":1574},[623],[568,3908,3910],{"className":3909},[1605],[568,3911,3913],{"className":3912},[628],[568,3914,1612],{"className":3915},[639],[568,3917],{"className":3918},[1616],[568,3920],{"className":3921},[634,1620],[568,3923,593],{"className":3924},[639],[568,3926],{"className":3927,"style":635},[634],[568,3929,3931,3934,3938,3941,3944],{"className":3930},[619],[568,3932],{"className":3933,"style":714},[623],[568,3935,3937],{"className":3936},[628],"∣3∣",[568,3939],{"className":3940,"style":656},[634],[568,3942,599],{"className":3943},[660],[568,3945],{"className":3946,"style":656},[634],[568,3948,3950,3953,3957,3960,3963],{"className":3949},[619],[568,3951],{"className":3952,"style":714},[623],[568,3954,3956],{"className":3955},[628],"∣4∣",[568,3958],{"className":3959,"style":635},[634],[568,3961,593],{"className":3962},[639],[568,3964],{"className":3965,"style":635},[634],[568,3967,3969,3972],{"className":3968},[619],[568,3970],{"className":3971,"style":861},[623],[568,3973,3846],{"className":3974},[628],[798,3976,3977,3978,4034,4035,979],{},"Ein 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bi,\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:0.044em;\">z\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:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\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 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xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>z\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">z\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:0.044em;\">z\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":596,"meaning":4179,"symbolHtml":4180},"Realteil von z","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan 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