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z",[568,1038,1040,1058,1104],{"className":1039,"ariaHidden":615},[614],[568,1041,1043,1046,1049,1052,1055],{"className":1042},[619],[568,1044],{"className":1045,"style":649},[623],[568,1047,589],{"className":1048,"style":630},[628,629],[568,1050],{"className":1051,"style":656},[634],[568,1053,1014],{"className":1054},[660],[568,1056],{"className":1057,"style":656},[634],[568,1059,1061,1064,1095,1098,1101],{"className":1060},[619],[568,1062],{"className":1063,"style":713},[623],[568,1065,1067],{"className":1066},[628,717],[568,1068,1070],{"className":1069},[721],[568,1071,1073],{"className":1072},[725],[568,1074,1076,1087],{"className":1075,"style":713},[729],[568,1077,1078,1081],{"style":732},[568,1079],{"className":1080,"style":737},[736],[568,1082,1084],{"className":1083},[628],[568,1085,589],{"className":1086,"style":630},[628,629],[568,1088,1089,1092],{"style":746},[568,1090],{"className":1091,"style":737},[736],[568,1093],{"className":1094,"style":754},[753],[568,1096],{"className":1097,"style":635},[634],[568,1099,593],{"className":1100},[639],[568,1102],{"className":1103,"style":635},[634],[568,1105,1107,1110,1113,1116,1119,1125,1128],{"className":1106},[619],[568,1108],{"className":1109,"style":975},[623],[568,1111,889],{"className":1112},[628],[568,1114,605],{"className":1115},[628,629],[568,1117],{"className":1118,"style":982},[634],[568,1120,1122],{"className":1121},[986],[568,1123,1029],{"className":1124},[628,990],[568,1126],{"className":1127,"style":982},[634],[568,1129,589],{"className":1130,"style":630},[628,629],[860,1132,1133,997,1341],{},[568,1134,1136,1177],{"className":1135},[571],[568,1137,1139],{"className":1138},[575],[577,1140,1141],{"xmlns":579},[581,1142,1143,1174],{},[584,1144,1145,1158,1160,1166,1168],{},[694,1146,1147,1156],{"accent":615},[584,1148,1149,1151,1153],{},[587,1150,589],{},[591,1152,599],{},[587,1154,1155],{},"w",[591,1157,700],{"stretchy":615},[591,1159,593],{},[694,1161,1162,1164],{"accent":615},[587,1163,589],{},[591,1165,700],{"stretchy":615},[591,1167,599],{},[694,1169,1170,1172],{"accent":615},[587,1171,1155],{},[591,1173,700],{"stretchy":615},[607,1175,1176],{"encoding":609},"\\overline{z 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\\overline{w}",[568,1178,1180,1257,1304],{"className":1179,"ariaHidden":615},[614],[568,1181,1183,1187,1248,1251,1254],{"className":1182},[619],[568,1184],{"className":1185,"style":1186},[623],"height:0.8667em;vertical-align:-0.0833em;",[568,1188,1190],{"className":1189},[628,717],[568,1191,1194,1239],{"className":1192},[721,1193],"vlist-t2",[568,1195,1197,1234],{"className":1196},[725],[568,1198,1201,1225],{"className":1199,"style":1200},[729],"height:0.7833em;",[568,1202,1203,1206],{"style":732},[568,1204],{"className":1205,"style":737},[736],[568,1207,1209,1212,1215,1218,1221],{"className":1208},[628],[568,1210,589],{"className":1211,"style":630},[628,629],[568,1213],{"className":1214,"style":656},[634],[568,1216,599],{"className":1217},[660],[568,1219],{"className":1220,"style":656},[634],[568,1222,1155],{"className":1223,"style":1224},[628,629],"margin-right:0.0269em;",[568,1226,1228,1231],{"style":1227},"top:-3.7033em;",[568,1229],{"className":1230,"style":737},[736],[568,1232],{"className":1233,"style":754},[753],[568,1235,1238],{"className":1236},[1237],"vlist-s","​",[568,1240,1242],{"className":1241},[725],[568,1243,1246],{"className":1244,"style":1245},[729],"height:0.0833em;",[568,1247],{},[568,1249],{"className":1250,"style":635},[634],[568,1252,593],{"className":1253},[639],[568,1255],{"className":1256,"style":635},[634],[568,1258,1260,1264,1295,1298,1301],{"className":1259},[619],[568,1261],{"className":1262,"style":1263},[623],"height:0.7139em;vertical-align:-0.0833em;",[568,1265,1267],{"className":1266},[628,717],[568,1268,1270],{"className":1269},[721],[568,1271,1273],{"className":1272},[725],[568,1274,1276,1287],{"className":1275,"style":713},[729],[568,1277,1278,1281],{"style":732},[568,1279],{"className":1280,"style":737},[736],[568,1282,1284],{"className":1283},[628],[568,1285,589],{"className":1286,"style":630},[628,629],[568,1288,1289,1292],{"style":746},[568,1290],{"className":1291,"style":737},[736],[568,1293],{"className":1294,"style":754},[753],[568,1296],{"className":1297,"style":656},[634],[568,1299,599],{"className":1300},[660],[568,1302],{"className":1303,"style":656},[634],[568,1305,1307,1310],{"className":1306},[619],[568,1308],{"className":1309,"style":713},[623],[568,1311,1313],{"className":1312},[628,717],[568,1314,1316],{"className":1315},[721],[568,1317,1319],{"className":1318},[725],[568,1320,1322,1333],{"className":1321,"style":713},[729],[568,1323,1324,1327],{"style":732},[568,1325],{"className":1326,"style":737},[736],[568,1328,1330],{"className":1329},[628],[568,1331,1155],{"className":1332,"style":1224},[628,629],[568,1334,1335,1338],{"style":746},[568,1336],{"className":1337,"style":737},[736],[568,1339],{"className":1340,"style":754},[753],[568,1342,1344,1384],{"className":1343},[571],[568,1345,1347],{"className":1346},[575],[577,1348,1349],{"xmlns":579},[581,1350,1351,1381],{},[584,1352,1353,1365,1367,1373,1375],{},[694,1354,1355,1363],{"accent":615},[584,1356,1357,1359,1361],{},[587,1358,589],{},[591,1360,779],{},[587,1362,1155],{},[591,1364,700],{"stretchy":615},[591,1366,593],{},[694,1368,1369,1371],{"accent":615},[587,1370,589],{},[591,1372,700],{"stretchy":615},[591,1374,779],{},[694,1376,1377,1379],{"accent":615},[587,1378,1155],{},[591,1380,700],{"stretchy":615},[607,1382,1383],{"encoding":609},"\\overline{z \\cdot w} = \\overline{z} \\cdot \\overline{w}",[568,1385,1387,1447,1493],{"className":1386,"ariaHidden":615},[614],[568,1388,1390,1394,1438,1441,1444],{"className":1389},[619],[568,1391],{"className":1392,"style":1393},[623],"height:0.6445em;",[568,1395,1397],{"className":1396},[628,717],[568,1398,1400],{"className":1399},[721],[568,1401,1403],{"className":1402},[725],[568,1404,1406,1429],{"className":1405,"style":1393},[729],[568,1407,1408,1411],{"style":732},[568,1409],{"className":1410,"style":737},[736],[568,1412,1414,1417,1420,1423,1426],{"className":1413},[628],[568,1415,589],{"className":1416,"style":630},[628,629],[568,1418],{"className":1419,"style":656},[634],[568,1421,779],{"className":1422},[660],[568,1424],{"className":1425,"style":656},[634],[568,1427,1155],{"className":1428,"style":1224},[628,629],[568,1430,1432,1435],{"style":1431},"top:-3.5644em;",[568,1433],{"className":1434,"style":737},[736],[568,1436],{"className":1437,"style":754},[753],[568,1439],{"className":1440,"style":635},[634],[568,1442,593],{"className":1443},[639],[568,1445],{"className":1446,"style":635},[634],[568,1448,1450,1453,1484,1487,1490],{"className":1449},[619],[568,1451],{"className":1452,"style":713},[623],[568,1454,1456],{"className":1455},[628,717],[568,1457,1459],{"className":1458},[721],[568,1460,1462],{"className":1461},[725],[568,1463,1465,1476],{"className":1464,"style":713},[729],[568,1466,1467,1470],{"style":732},[568,1468],{"className":1469,"style":737},[736],[568,1471,1473],{"className":1472},[628],[568,1474,589],{"className":1475,"style":630},[628,629],[568,1477,1478,1481],{"style":746},[568,1479],{"className":1480,"style":737},[736],[568,1482],{"className":1483,"style":754},[753],[568,1485],{"className":1486,"style":656},[634],[568,1488,779],{"className":1489},[660],[568,1491],{"className":1492,"style":656},[634],[568,1494,1496,1499],{"className":1495},[619],[568,1497],{"className":1498,"style":713},[623],[568,1500,1502],{"className":1501},[628,717],[568,1503,1505],{"className":1504},[721],[568,1506,1508],{"className":1507},[725],[568,1509,1511,1522],{"className":1510,"style":713},[729],[568,1512,1513,1516],{"style":732},[568,1514],{"className":1515,"style":737},[736],[568,1517,1519],{"className":1518},[628],[568,1520,1155],{"className":1521,"style":1224},[628,629],[568,1523,1524,1527],{"style":746},[568,1525],{"className":1526,"style":737},[736],[568,1528],{"className":1529,"style":754},[753],[860,1531,1532,1649,1650,1733,1734,1762],{},[568,1533,1535,1561],{"className":1534},[571],[568,1536,1538],{"className":1537},[575],[577,1539,1540],{"xmlns":579},[581,1541,1542,1558],{},[584,1543,1544,1554,1556],{},[694,1545,1546,1552],{"accent":615},[694,1547,1548,1550],{"accent":615},[587,1549,589],{},[591,1551,700],{"stretchy":615},[591,1553,700],{"stretchy":615},[591,1555,593],{},[587,1557,589],{},[607,1559,1560],{"encoding":609},"\\overline{\\overline{z}} = z",[568,1562,1564,1640],{"className":1563,"ariaHidden":615},[614],[568,1565,1567,1571,1631,1634,1637],{"className":1566},[619],[568,1568],{"className":1569,"style":1570},[623],"height:0.8306em;",[568,1572,1574],{"className":1573},[628,717],[568,1575,1577],{"className":1576},[721],[568,1578,1580],{"className":1579},[725],[568,1581,1583,1622],{"className":1582,"style":1570},[729],[568,1584,1585,1588],{"style":732},[568,1586],{"className":1587,"style":737},[736],[568,1589,1591],{"className":1590},[628],[568,1592,1594],{"className":1593},[628,717],[568,1595,1597],{"className":1596},[721],[568,1598,1600],{"className":1599},[725],[568,1601,1603,1614],{"className":1602,"style":713},[729],[568,1604,1605,1608],{"style":732},[568,1606],{"className":1607,"style":737},[736],[568,1609,1611],{"className":1610},[628],[568,1612,589],{"className":1613,"style":630},[628,629],[568,1615,1616,1619],{"style":746},[568,1617],{"className":1618,"style":737},[736],[568,1620],{"className":1621,"style":754},[753],[568,1623,1625,1628],{"style":1624},"top:-3.7506em;",[568,1626],{"className":1627,"style":737},[736],[568,1629],{"className":1630,"style":754},[753],[568,1632],{"className":1633,"style":635},[634],[568,1635,593],{"className":1636},[639],[568,1638],{"className":1639,"style":635},[634],[568,1641,1643,1646],{"className":1642},[619],[568,1644],{"className":1645,"style":624},[623],[568,1647,589],{"className":1648,"style":630},[628,629],", und ",[568,1651,1653,1675],{"className":1652},[571],[568,1654,1656],{"className":1655},[575],[577,1657,1658],{"xmlns":579},[581,1659,1660,1672],{},[584,1661,1662,1664,1666],{},[587,1663,589],{},[591,1665,593],{},[694,1667,1668,1670],{"accent":615},[587,1669,589],{},[591,1671,700],{"stretchy":615},[607,1673,1674],{"encoding":609},"z = \\overline{z}",[568,1676,1678,1696],{"className":1677,"ariaHidden":615},[614],[568,1679,1681,1684,1687,1690,1693],{"className":1680},[619],[568,1682],{"className":1683,"style":624},[623],[568,1685,589],{"className":1686,"style":630},[628,629],[568,1688],{"className":1689,"style":635},[634],[568,1691,593],{"className":1692},[639],[568,1694],{"className":1695,"style":635},[634],[568,1697,1699,1702],{"className":1698},[619],[568,1700],{"className":1701,"style":713},[623],[568,1703,1705],{"className":1704},[628,717],[568,1706,1708],{"className":1707},[721],[568,1709,1711],{"className":1710},[725],[568,1712,1714,1725],{"className":1713,"style":713},[729],[568,1715,1716,1719],{"style":732},[568,1717],{"className":1718,"style":737},[736],[568,1720,1722],{"className":1721},[628],[568,1723,589],{"className":1724,"style":630},[628,629],[568,1726,1727,1730],{"style":746},[568,1728],{"className":1729,"style":737},[736],[568,1731],{"className":1732,"style":754},[753]," gilt genau dann, wenn ",[568,1735,1737,1750],{"className":1736},[571],[568,1738,1740],{"className":1739},[575],[577,1741,1742],{"xmlns":579},[581,1743,1744,1748],{},[584,1745,1746],{},[587,1747,589],{},[607,1749,589],{"encoding":609},[568,1751,1753],{"className":1752,"ariaHidden":615},[614],[568,1754,1756,1759],{"className":1755},[619],[568,1757],{"className":1758,"style":624},[623],[568,1760,589],{"className":1761,"style":630},[628,629]," reell ist.",[564,1764,1765,1766,680,1769,1797,1798,1858],{},"Hat ein Polynom nur reelle Koeffizienten, treten seine nicht reellen Nullstellen immer als ",[677,1767,1768],{},"konjugierte Paare",[568,1770,1772,1785],{"className":1771},[571],[568,1773,1775],{"className":1774},[575],[577,1776,1777],{"xmlns":579},[581,1778,1779,1783],{},[584,1780,1781],{},[587,1782,589],{},[607,1784,589],{"encoding":609},[568,1786,1788],{"className":1787,"ariaHidden":615},[614],[568,1789,1791,1794],{"className":1790},[619],[568,1792],{"className":1793,"style":624},[623],[568,1795,589],{"className":1796,"style":630},[628,629],", ",[568,1799,1801,1818],{"className":1800},[571],[568,1802,1804],{"className":1803},[575],[577,1805,1806],{"xmlns":579},[581,1807,1808,1816],{},[584,1809,1810],{},[694,1811,1812,1814],{"accent":615},[587,1813,589],{},[591,1815,700],{"stretchy":615},[607,1817,703],{"encoding":609},[568,1819,1821],{"className":1820,"ariaHidden":615},[614],[568,1822,1824,1827],{"className":1823},[619],[568,1825],{"className":1826,"style":713},[623],[568,1828,1830],{"className":1829},[628,717],[568,1831,1833],{"className":1832},[721],[568,1834,1836],{"className":1835},[725],[568,1837,1839,1850],{"className":1838,"style":713},[729],[568,1840,1841,1844],{"style":732},[568,1842],{"className":1843,"style":737},[736],[568,1845,1847],{"className":1846},[628],[568,1848,589],{"className":1849,"style":630},[628,629],[568,1851,1852,1855],{"style":746},[568,1853],{"className":1854,"style":737},[736],[568,1856],{"className":1857,"style":754},[753]," auf.",[559,1860,1862],{"id":1861},"herleitung","Herleitung",[568,1864,1867],{"className":1865},[1866],"katex-display",[568,1868,1870,1983],{"className":1869},[571],[568,1871,1873],{"className":1872},[575],[577,1874,1876],{"xmlns":579,"display":1875},"block",[581,1877,1878,1980],{},[584,1879,1880,1882,1884,1890,1892,1896,1898,1900,1902,1904,1907,1909,1911,1913,1915,1917,1919,1921,1928,1930,1932,1934,1936,1942,1944,1950,1952,1958,1964,1966,1972,1974],{},[587,1881,589],{},[591,1883,779],{},[694,1885,1886,1888],{"accent":615},[587,1887,589],{},[591,1889,700],{"stretchy":615},[591,1891,593],{},[591,1893,1895],{"stretchy":1894},"false","(",[587,1897,596],{},[591,1899,599],{},[587,1901,602],{},[587,1903,605],{},[591,1905,1906],{"stretchy":1894},")",[591,1908,1895],{"stretchy":1894},[587,1910,596],{},[591,1912,1014],{},[587,1914,602],{},[587,1916,605],{},[591,1918,1906],{"stretchy":1894},[591,1920,593],{},[1922,1923,1924,1926],"msup",{},[587,1925,596],{},[887,1927,889],{},[591,1929,1014],{},[591,1931,1895],{"stretchy":1894},[587,1933,602],{},[587,1935,605],{},[1922,1937,1938,1940],{},[591,1939,1906],{"stretchy":1894},[887,1941,889],{},[591,1943,593],{},[1922,1945,1946,1948],{},[587,1947,596],{},[887,1949,889],{},[591,1951,1014],{},[1922,1953,1954,1956],{},[587,1955,602],{},[887,1957,889],{},[1922,1959,1960,1962],{},[587,1961,605],{},[887,1963,889],{},[591,1965,593],{},[1922,1967,1968,1970],{},[587,1969,596],{},[887,1971,889],{},[591,1973,599],{},[1922,1975,1976,1978],{},[587,1977,602],{},[887,1979,889],{},[607,1981,1982],{"encoding":609},"z \\cdot \\overline{z} = (a + bi)(a - bi) = a^2 - (bi)^2 = a^2 - b^2 i^2 = a^2 + b^2",[568,1984,1986,2004,2050,2073,2101,2122,2175,2226,2270,2343,2387],{"className":1985,"ariaHidden":615},[614],[568,1987,1989,1992,1995,1998,2001],{"className":1988},[619],[568,1990],{"className":1991,"style":798},[623],[568,1993,589],{"className":1994,"style":630},[628,629],[568,1996],{"className":1997,"style":656},[634],[568,1999,779],{"className":2000},[660],[568,2002],{"className":2003,"style":656},[634],[568,2005,2007,2010,2041,2044,2047],{"className":2006},[619],[568,2008],{"className":2009,"style":713},[623],[568,2011,2013],{"className":2012},[628,717],[568,2014,2016],{"className":2015},[721],[568,2017,2019],{"className":2018},[725],[568,2020,2022,2033],{"className":2021,"style":713},[729],[568,2023,2024,2027],{"style":732},[568,2025],{"className":2026,"style":737},[736],[568,2028,2030],{"className":2029},[628],[568,2031,589],{"className":2032,"style":630},[628,629],[568,2034,2035,2038],{"style":746},[568,2036],{"className":2037,"style":737},[736],[568,2039],{"className":2040,"style":754},[753],[568,2042],{"className":2043,"style":635},[634],[568,2045,593],{"className":2046},[639],[568,2048],{"className":2049,"style":635},[634],[568,2051,2053,2057,2061,2064,2067,2070],{"className":2052},[619],[568,2054],{"className":2055,"style":2056},[623],"height:1em;vertical-align:-0.25em;",[568,2058,1895],{"className":2059},[2060],"mopen",[568,2062,596],{"className":2063},[628,629],[568,2065],{"className":2066,"style":656},[634],[568,2068,599],{"className":2069},[660],[568,2071],{"className":2072,"style":656},[634],[568,2074,2076,2079,2082,2086,2089,2092,2095,2098],{"className":2075},[619],[568,2077],{"className":2078,"style":2056},[623],[568,2080,674],{"className":2081},[628,629],[568,2083,1906],{"className":2084},[2085],"mclose",[568,2087,1895],{"className":2088},[2060],[568,2090,596],{"className":2091},[628,629],[568,2093],{"className":2094,"style":656},[634],[568,2096,1014],{"className":2097},[660],[568,2099],{"className":2100,"style":656},[634],[568,2102,2104,2107,2110,2113,2116,2119],{"className":2103},[619],[568,2105],{"className":2106,"style":2056},[623],[568,2108,674],{"className":2109},[628,629],[568,2111,1906],{"className":2112},[2085],[568,2114],{"className":2115,"style":635},[634],[568,2117,593],{"className":2118},[639],[568,2120],{"className":2121,"style":635},[634],[568,2123,2125,2129,2166,2169,2172],{"className":2124},[619],[568,2126],{"className":2127,"style":2128},[623],"height:0.9474em;vertical-align:-0.0833em;",[568,2130,2132,2135],{"className":2131},[628],[568,2133,596],{"className":2134},[628,629],[568,2136,2139],{"className":2137},[2138],"msupsub",[568,2140,2142],{"className":2141},[721],[568,2143,2145],{"className":2144},[725],[568,2146,2149],{"className":2147,"style":2148},[729],"height:0.8641em;",[568,2150,2152,2156],{"style":2151},"top:-3.113em;margin-right:0.05em;",[568,2153],{"className":2154,"style":2155},[736],"height:2.7em;",[568,2157,2163],{"className":2158},[2159,2160,2161,2162],"sizing","reset-size6","size3","mtight",[568,2164,889],{"className":2165},[628,2162],[568,2167],{"className":2168,"style":656},[634],[568,2170,1014],{"className":2171},[660],[568,2173],{"className":2174,"style":656},[634],[568,2176,2178,2182,2185,2188,2217,2220,2223],{"className":2177},[619],[568,2179],{"className":2180,"style":2181},[623],"height:1.1141em;vertical-align:-0.25em;",[568,2183,1895],{"className":2184},[2060],[568,2186,674],{"className":2187},[628,629],[568,2189,2191,2194],{"className":2190},[2085],[568,2192,1906],{"className":2193},[2085],[568,2195,2197],{"className":2196},[2138],[568,2198,2200],{"className":2199},[721],[568,2201,2203],{"className":2202},[725],[568,2204,2206],{"className":2205,"style":2148},[729],[568,2207,2208,2211],{"style":2151},[568,2209],{"className":2210,"style":2155},[736],[568,2212,2214],{"className":2213},[2159,2160,2161,2162],[568,2215,889],{"className":2216},[628,2162],[568,2218],{"className":2219,"style":635},[634],[568,2221,593],{"className":2222},[639],[568,2224],{"className":2225,"style":635},[634],[568,2227,2229,2232,2261,2264,2267],{"className":2228},[619],[568,2230],{"className":2231,"style":2128},[623],[568,2233,2235,2238],{"className":2234},[628],[568,2236,596],{"className":2237},[628,629],[568,2239,2241],{"className":2240},[2138],[568,2242,2244],{"className":2243},[721],[568,2245,2247],{"className":2246},[725],[568,2248,2250],{"className":2249,"style":2148},[729],[568,2251,2252,2255],{"style":2151},[568,2253],{"className":2254,"style":2155},[736],[568,2256,2258],{"className":2257},[2159,2160,2161,2162],[568,2259,889],{"className":2260},[628,2162],[568,2262],{"className":2263,"style":656},[634],[568,2265,1014],{"className":2266},[660],[568,2268],{"className":2269,"style":656},[634],[568,2271,2273,2276,2305,2334,2337,2340],{"className":2272},[619],[568,2274],{"className":2275,"style":2148},[623],[568,2277,2279,2282],{"className":2278},[628],[568,2280,602],{"className":2281},[628,629],[568,2283,2285],{"className":2284},[2138],[568,2286,2288],{"className":2287},[721],[568,2289,2291],{"className":2290},[725],[568,2292,2294],{"className":2293,"style":2148},[729],[568,2295,2296,2299],{"style":2151},[568,2297],{"className":2298,"style":2155},[736],[568,2300,2302],{"className":2301},[2159,2160,2161,2162],[568,2303,889],{"className":2304},[628,2162],[568,2306,2308,2311],{"className":2307},[628],[568,2309,605],{"className":2310},[628,629],[568,2312,2314],{"className":2313},[2138],[568,2315,2317],{"className":2316},[721],[568,2318,2320],{"className":2319},[725],[568,2321,2323],{"className":2322,"style":2148},[729],[568,2324,2325,2328],{"style":2151},[568,2326],{"className":2327,"style":2155},[736],[568,2329,2331],{"className":2330},[2159,2160,2161,2162],[568,2332,889],{"className":2333},[628,2162],[568,2335],{"className":2336,"style":635},[634],[568,2338,593],{"className":2339},[639],[568,2341],{"className":2342,"style":635},[634],[568,2344,2346,2349,2378,2381,2384],{"className":2345},[619],[568,2347],{"className":2348,"style":2128},[623],[568,2350,2352,2355],{"className":2351},[628],[568,2353,596],{"className":2354},[628,629],[568,2356,2358],{"className":2357},[2138],[568,2359,2361],{"className":2360},[721],[568,2362,2364],{"className":2363},[725],[568,2365,2367],{"className":2366,"style":2148},[729],[568,2368,2369,2372],{"style":2151},[568,2370],{"className":2371,"style":2155},[736],[568,2373,2375],{"className":2374},[2159,2160,2161,2162],[568,2376,889],{"className":2377},[628,2162],[568,2379],{"className":2380,"style":656},[634],[568,2382,599],{"className":2383},[660],[568,2385],{"className":2386,"style":656},[634],[568,2388,2390,2393],{"className":2389},[619],[568,2391],{"className":2392,"style":2148},[623],[568,2394,2396,2399],{"className":2395},[628],[568,2397,602],{"className":2398},[628,629],[568,2400,2402],{"className":2401},[2138],[568,2403,2405],{"className":2404},[721],[568,2406,2408],{"className":2407},[725],[568,2409,2411],{"className":2410,"style":2148},[729],[568,2412,2413,2416],{"style":2151},[568,2414],{"className":2415,"style":2155},[736],[568,2417,2419],{"className":2418},[2159,2160,2161,2162],[568,2420,889],{"className":2421},[628,2162],[564,2423,2424,2425,759],{},"Das ist die dritte binomische Formel mit ",[568,2426,2428,2453],{"className":2427},[571],[568,2429,2431],{"className":2430},[575],[577,2432,2433],{"xmlns":579},[581,2434,2435,2450],{},[584,2436,2437,2443,2445,2447],{},[1922,2438,2439,2441],{},[587,2440,605],{},[887,2442,889],{},[591,2444,593],{},[591,2446,1014],{},[887,2448,2449],{},"1",[607,2451,2452],{"encoding":609},"i^2 = -1",[568,2454,2456,2502],{"className":2455,"ariaHidden":615},[614],[568,2457,2459,2463,2493,2496,2499],{"className":2458},[619],[568,2460],{"className":2461,"style":2462},[623],"height:0.8141em;",[568,2464,2466,2469],{"className":2465},[628],[568,2467,605],{"className":2468},[628,629],[568,2470,2472],{"className":2471},[2138],[568,2473,2475],{"className":2474},[721],[568,2476,2478],{"className":2477},[725],[568,2479,2481],{"className":2480,"style":2462},[729],[568,2482,2484,2487],{"style":2483},"top:-3.063em;margin-right:0.05em;",[568,2485],{"className":2486,"style":2155},[736],[568,2488,2490],{"className":2489},[2159,2160,2161,2162],[568,2491,889],{"className":2492},[628,2162],[568,2494],{"className":2495,"style":635},[634],[568,2497,593],{"className":2498},[639],[568,2500],{"className":2501,"style":635},[634],[568,2503,2505,2509,2512],{"className":2504},[619],[568,2506],{"className":2507,"style":2508},[623],"height:0.7278em;vertical-align:-0.0833em;",[568,2510,1014],{"className":2511},[628],[568,2513,2449],{"className":2514},[628],[559,2516,2518],{"id":2517},"beispiele","Beispiele",[564,2520,2521,2522,2603,2604,2714],{},"Für ",[568,2523,2525,2551],{"className":2524},[571],[568,2526,2528],{"className":2527},[575],[577,2529,2530],{"xmlns":579},[581,2531,2532,2548],{},[584,2533,2534,2536,2538,2541,2543,2546],{},[587,2535,589],{},[591,2537,593],{},[887,2539,2540],{},"3",[591,2542,599],{},[887,2544,2545],{},"4",[587,2547,605],{},[607,2549,2550],{"encoding":609},"z = 3 + 4i",[568,2552,2554,2572,2590],{"className":2553,"ariaHidden":615},[614],[568,2555,2557,2560,2563,2566,2569],{"className":2556},[619],[568,2558],{"className":2559,"style":624},[623],[568,2561,589],{"className":2562,"style":630},[628,629],[568,2564],{"className":2565,"style":635},[634],[568,2567,593],{"className":2568},[639],[568,2570],{"className":2571,"style":635},[634],[568,2573,2575,2578,2581,2584,2587],{"className":2574},[619],[568,2576],{"className":2577,"style":2508},[623],[568,2579,2540],{"className":2580},[628],[568,2582],{"className":2583,"style":656},[634],[568,2585,599],{"className":2586},[660],[568,2588],{"className":2589,"style":656},[634],[568,2591,2593,2597,2600],{"className":2592},[619],[568,2594],{"className":2595,"style":2596},[623],"height:0.6595em;",[568,2598,2545],{"className":2599},[628],[568,2601,605],{"className":2602},[628,629]," ist ",[568,2605,2607,2635],{"className":2606},[571],[568,2608,2610],{"className":2609},[575],[577,2611,2612],{"xmlns":579},[581,2613,2614,2632],{},[584,2615,2616,2622,2624,2626,2628,2630],{},[694,2617,2618,2620],{"accent":615},[587,2619,589],{},[591,2621,700],{"stretchy":615},[591,2623,593],{},[887,2625,2540],{},[591,2627,1014],{},[887,2629,2545],{},[587,2631,605],{},[607,2633,2634],{"encoding":609},"\\overline{z} = 3 - 4i",[568,2636,2638,2684,2702],{"className":2637,"ariaHidden":615},[614],[568,2639,2641,2644,2675,2678,2681],{"className":2640},[619],[568,2642],{"className":2643,"style":713},[623],[568,2645,2647],{"className":2646},[628,717],[568,2648,2650],{"className":2649},[721],[568,2651,2653],{"className":2652},[725],[568,2654,2656,2667],{"className":2655,"style":713},[729],[568,2657,2658,2661],{"style":732},[568,2659],{"className":2660,"style":737},[736],[568,2662,2664],{"className":2663},[628],[568,2665,589],{"className":2666,"style":630},[628,629],[568,2668,2669,2672],{"style":746},[568,2670],{"className":2671,"style":737},[736],[568,2673],{"className":2674,"style":754},[753],[568,2676],{"className":2677,"style":635},[634],[568,2679,593],{"className":2680},[639],[568,2682],{"className":2683,"style":635},[634],[568,2685,2687,2690,2693,2696,2699],{"className":2686},[619],[568,2688],{"className":2689,"style":2508},[623],[568,2691,2540],{"className":2692},[628],[568,2694],{"className":2695,"style":656},[634],[568,2697,1014],{"className":2698},[660],[568,2700],{"className":2701,"style":656},[634],[568,2703,2705,2708,2711],{"className":2704},[619],[568,2706],{"className":2707,"style":2596},[623],[568,2709,2545],{"className":2710},[628],[568,2712,605],{"className":2713},[628,629]," und",[568,2716,2718],{"className":2717},[1866],[568,2719,2721,2792],{"className":2720},[571],[568,2722,2724],{"className":2723},[575],[577,2725,2726],{"xmlns":579,"display":1875},[581,2727,2728,2789],{},[584,2729,2730,2732,2734,2740,2742,2745,2747,2750,2752,2755,2757,2760,2762,2768,2771,2774,2776,2778,2784,2786],{},[587,2731,589],{},[591,2733,779],{},[694,2735,2736,2738],{"accent":615},[587,2737,589],{},[591,2739,700],{"stretchy":615},[591,2741,593],{},[887,2743,2744],{},"9",[591,2746,599],{},[887,2748,2749],{},"16",[591,2751,593],{},[887,2753,2754],{},"25",[591,2756,593],{},[587,2758,2759],{"mathvariant":892},"∣",[587,2761,589],{},[1922,2763,2764,2766],{},[587,2765,2759],{"mathvariant":892},[887,2767,889],{},[591,2769,2770],{"separator":615},",",[634,2772],{"width":2773},"2em",[587,2775,589],{},[591,2777,599],{},[694,2779,2780,2782],{"accent":615},[587,2781,589],{},[591,2783,700],{"stretchy":615},[591,2785,593],{},[887,2787,2788],{},"6",[607,2790,2791],{"encoding":609},"z \\cdot \\overline{z} = 9 + 16 = 25 = |z|^2, \\qquad z + \\overline{z} = 6",[568,2793,2795,2813,2859,2877,2896,2914,2978,3024],{"className":2794,"ariaHidden":615},[614],[568,2796,2798,2801,2804,2807,2810],{"className":2797},[619],[568,2799],{"className":2800,"style":798},[623],[568,2802,589],{"className":2803,"style":630},[628,629],[568,2805],{"className":2806,"style":656},[634],[568,2808,779],{"className":2809},[660],[568,2811],{"className":2812,"style":656},[634],[568,2814,2816,2819,2850,2853,2856],{"className":2815},[619],[568,2817],{"className":2818,"style":713},[623],[568,2820,2822],{"className":2821},[628,717],[568,2823,2825],{"className":2824},[721],[568,2826,2828],{"className":2827},[725],[568,2829,2831,2842],{"className":2830,"style":713},[729],[568,2832,2833,2836],{"style":732},[568,2834],{"className":2835,"style":737},[736],[568,2837,2839],{"className":2838},[628],[568,2840,589],{"className":2841,"style":630},[628,629],[568,2843,2844,2847],{"style":746},[568,2845],{"className":2846,"style":737},[736],[568,2848],{"className":2849,"style":754},[753],[568,2851],{"className":2852,"style":635},[634],[568,2854,593],{"className":2855},[639],[568,2857],{"className":2858,"style":635},[634],[568,2860,2862,2865,2868,2871,2874],{"className":2861},[619],[568,2863],{"className":2864,"style":2508},[623],[568,2866,2744],{"className":2867},[628],[568,2869],{"className":2870,"style":656},[634],[568,2872,599],{"className":2873},[660],[568,2875],{"className":2876,"style":656},[634],[568,2878,2880,2884,2887,2890,2893],{"className":2879},[619],[568,2881],{"className":2882,"style":2883},[623],"height:0.6444em;",[568,2885,2749],{"className":2886},[628],[568,2888],{"className":2889,"style":635},[634],[568,2891,593],{"className":2892},[639],[568,2894],{"className":2895,"style":635},[634],[568,2897,2899,2902,2905,2908,2911],{"className":2898},[619],[568,2900],{"className":2901,"style":2883},[623],[568,2903,2754],{"className":2904},[628],[568,2906],{"className":2907,"style":635},[634],[568,2909,593],{"className":2910},[639],[568,2912],{"className":2913,"style":635},[634],[568,2915,2917,2920,2923,2926,2955,2959,2963,2966,2969,2972,2975],{"className":2916},[619],[568,2918],{"className":2919,"style":2181},[623],[568,2921,2759],{"className":2922},[628],[568,2924,589],{"className":2925,"style":630},[628,629],[568,2927,2929,2932],{"className":2928},[628],[568,2930,2759],{"className":2931},[628],[568,2933,2935],{"className":2934},[2138],[568,2936,2938],{"className":2937},[721],[568,2939,2941],{"className":2940},[725],[568,2942,2944],{"className":2943,"style":2148},[729],[568,2945,2946,2949],{"style":2151},[568,2947],{"className":2948,"style":2155},[736],[568,2950,2952],{"className":2951},[2159,2160,2161,2162],[568,2953,889],{"className":2954},[628,2162],[568,2956,2770],{"className":2957},[2958],"mpunct",[568,2960],{"className":2961,"style":2962},[634],"margin-right:2em;",[568,2964],{"className":2965,"style":982},[634],[568,2967,589],{"className":2968,"style":630},[628,629],[568,2970],{"className":2971,"style":656},[634],[568,2973,599],{"className":2974},[660],[568,2976],{"className":2977,"style":656},[634],[568,2979,2981,2984,3015,3018,3021],{"className":2980},[619],[568,2982],{"className":2983,"style":713},[623],[568,2985,2987],{"className":2986},[628,717],[568,2988,2990],{"className":2989},[721],[568,2991,2993],{"className":2992},[725],[568,2994,2996,3007],{"className":2995,"style":713},[729],[568,2997,2998,3001],{"style":732},[568,2999],{"className":3000,"style":737},[736],[568,3002,3004],{"className":3003},[628],[568,3005,589],{"className":3006,"style":630},[628,629],[568,3008,3009,3012],{"style":746},[568,3010],{"className":3011,"style":737},[736],[568,3013],{"className":3014,"style":754},[753],[568,3016],{"className":3017,"style":635},[634],[568,3019,593],{"className":3020},[639],[568,3022],{"className":3023,"style":635},[634],[568,3025,3027,3030],{"className":3026},[619],[568,3028],{"className":3029,"style":2883},[623],[568,3031,2788],{"className":3032},[628],[564,3034,2521,3035,2603,3119,759],{},[568,3036,3038,3065],{"className":3037},[571],[568,3039,3041],{"className":3040},[575],[577,3042,3043],{"xmlns":579},[581,3044,3045,3062],{},[584,3046,3047,3049,3051,3053,3055,3057,3060],{},[587,3048,589],{},[591,3050,593],{},[591,3052,1014],{},[887,3054,889],{},[591,3056,1014],{},[887,3058,3059],{},"5",[587,3061,605],{},[607,3063,3064],{"encoding":609},"z = -2 - 5i",[568,3066,3068,3086,3107],{"className":3067,"ariaHidden":615},[614],[568,3069,3071,3074,3077,3080,3083],{"className":3070},[619],[568,3072],{"className":3073,"style":624},[623],[568,3075,589],{"className":3076,"style":630},[628,629],[568,3078],{"className":3079,"style":635},[634],[568,3081,593],{"className":3082},[639],[568,3084],{"className":3085,"style":635},[634],[568,3087,3089,3092,3095,3098,3101,3104],{"className":3088},[619],[568,3090],{"className":3091,"style":2508},[623],[568,3093,1014],{"className":3094},[628],[568,3096,889],{"className":3097},[628],[568,3099],{"className":3100,"style":656},[634],[568,3102,1014],{"className":3103},[660],[568,3105],{"className":3106,"style":656},[634],[568,3108,3110,3113,3116],{"className":3109},[619],[568,3111],{"className":3112,"style":2596},[623],[568,3114,3059],{"className":3115},[628],[568,3117,605],{"className":3118},[628,629],[568,3120,3122,3152],{"className":3121},[571],[568,3123,3125],{"className":3124},[575],[577,3126,3127],{"xmlns":579},[581,3128,3129,3149],{},[584,3130,3131,3137,3139,3141,3143,3145,3147],{},[694,3132,3133,3135],{"accent":615},[587,3134,589],{},[591,3136,700],{"stretchy":615},[591,3138,593],{},[591,3140,1014],{},[887,3142,889],{},[591,3144,599],{},[887,3146,3059],{},[587,3148,605],{},[607,3150,3151],{"encoding":609},"\\overline{z} = -2 + 5i",[568,3153,3155,3201,3222],{"className":3154,"ariaHidden":615},[614],[568,3156,3158,3161,3192,3195,3198],{"className":3157},[619],[568,3159],{"className":3160,"style":713},[623],[568,3162,3164],{"className":3163},[628,717],[568,3165,3167],{"className":3166},[721],[568,3168,3170],{"className":3169},[725],[568,3171,3173,3184],{"className":3172,"style":713},[729],[568,3174,3175,3178],{"style":732},[568,3176],{"className":3177,"style":737},[736],[568,3179,3181],{"className":3180},[628],[568,3182,589],{"className":3183,"style":630},[628,629],[568,3185,3186,3189],{"style":746},[568,3187],{"className":3188,"style":737},[736],[568,3190],{"className":3191,"style":754},[753],[568,3193],{"className":3194,"style":635},[634],[568,3196,593],{"className":3197},[639],[568,3199],{"className":3200,"style":635},[634],[568,3202,3204,3207,3210,3213,3216,3219],{"className":3203},[619],[568,3205],{"className":3206,"style":2508},[623],[568,3208,1014],{"className":3209},[628],[568,3211,889],{"className":3212},[628],[568,3214],{"className":3215,"style":656},[634],[568,3217,599],{"className":3218},[660],[568,3220],{"className":3221,"style":656},[634],[568,3223,3225,3228,3231],{"className":3224},[619],[568,3226],{"className":3227,"style":2596},[623],[568,3229,3059],{"className":3230},[628],[568,3232,605],{"className":3233},[628,629],[564,3235,3236,3237,3371,3372,759],{},"Die Gleichung ",[568,3238,3240,3275],{"className":3239},[571],[568,3241,3243],{"className":3242},[575],[577,3244,3245],{"xmlns":579},[581,3246,3247,3272],{},[584,3248,3249,3256,3258,3260,3262,3264,3267,3269],{},[1922,3250,3251,3254],{},[587,3252,3253],{},"x",[887,3255,889],{},[591,3257,1014],{},[887,3259,2545],{},[587,3261,3253],{},[591,3263,599],{},[887,3265,3266],{},"13",[591,3268,593],{},[887,3270,3271],{},"0",[607,3273,3274],{"encoding":609},"x^2 - 4x + 13 = 0",[568,3276,3278,3323,3344,3362],{"className":3277,"ariaHidden":615},[614],[568,3279,3281,3285,3314,3317,3320],{"className":3280},[619],[568,3282],{"className":3283,"style":3284},[623],"height:0.8974em;vertical-align:-0.0833em;",[568,3286,3288,3291],{"className":3287},[628],[568,3289,3253],{"className":3290},[628,629],[568,3292,3294],{"className":3293},[2138],[568,3295,3297],{"className":3296},[721],[568,3298,3300],{"className":3299},[725],[568,3301,3303],{"className":3302,"style":2462},[729],[568,3304,3305,3308],{"style":2483},[568,3306],{"className":3307,"style":2155},[736],[568,3309,3311],{"className":3310},[2159,2160,2161,2162],[568,3312,889],{"className":3313},[628,2162],[568,3315],{"className":3316,"style":656},[634],[568,3318,1014],{"className":3319},[660],[568,3321],{"className":3322,"style":656},[634],[568,3324,3326,3329,3332,3335,3338,3341],{"className":3325},[619],[568,3327],{"className":3328,"style":2508},[623],[568,3330,2545],{"className":3331},[628],[568,3333,3253],{"className":3334},[628,629],[568,3336],{"className":3337,"style":656},[634],[568,3339,599],{"className":3340},[660],[568,3342],{"className":3343,"style":656},[634],[568,3345,3347,3350,3353,3356,3359],{"className":3346},[619],[568,3348],{"className":3349,"style":2883},[623],[568,3351,3266],{"className":3352},[628],[568,3354],{"className":3355,"style":635},[634],[568,3357,593],{"className":3358},[639],[568,3360],{"className":3361,"style":635},[634],[568,3363,3365,3368],{"className":3364},[619],[568,3366],{"className":3367,"style":2883},[623],[568,3369,3271],{"className":3370},[628]," hat die konjugierten Lösungen ",[568,3373,3375,3411],{"className":3374},[571],[568,3376,3378],{"className":3377},[575],[577,3379,3380],{"xmlns":579},[581,3381,3382,3408],{},[584,3383,3384,3397,3399,3401,3404,3406],{},[3385,3386,3387,3389],"msub",{},[587,3388,3253],{},[584,3390,3391,3393,3395],{},[887,3392,2449],{},[591,3394,2770],{"separator":615},[887,3396,889],{},[591,3398,593],{},[887,3400,889],{},[591,3402,3403],{},"±",[887,3405,2540],{},[587,3407,605],{},[607,3409,3410],{"encoding":609},"x_{1,2} = 2 \\pm 3i",[568,3412,3414,3482,3500],{"className":3413,"ariaHidden":615},[614],[568,3415,3417,3421,3473,3476,3479],{"className":3416},[619],[568,3418],{"className":3419,"style":3420},[623],"height:0.7167em;vertical-align:-0.2861em;",[568,3422,3424,3427],{"className":3423},[628],[568,3425,3253],{"className":3426},[628,629],[568,3428,3430],{"className":3429},[2138],[568,3431,3433,3464],{"className":3432},[721,1193],[568,3434,3436,3461],{"className":3435},[725],[568,3437,3440],{"className":3438,"style":3439},[729],"height:0.3011em;",[568,3441,3443,3446],{"style":3442},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[568,3444],{"className":3445,"style":2155},[736],[568,3447,3449],{"className":3448},[2159,2160,2161,2162],[568,3450,3452,3455,3458],{"className":3451},[628,2162],[568,3453,2449],{"className":3454},[628,2162],[568,3456,2770],{"className":3457},[2958,2162],[568,3459,889],{"className":3460},[628,2162],[568,3462,1238],{"className":3463},[1237],[568,3465,3467],{"className":3466},[725],[568,3468,3471],{"className":3469,"style":3470},[729],"height:0.2861em;",[568,3472],{},[568,3474],{"className":3475,"style":635},[634],[568,3477,593],{"className":3478},[639],[568,3480],{"className":3481,"style":635},[634],[568,3483,3485,3488,3491,3494,3497],{"className":3484},[619],[568,3486],{"className":3487,"style":2508},[623],[568,3489,889],{"className":3490},[628],[568,3492],{"className":3493,"style":656},[634],[568,3495,3403],{"className":3496},[660],[568,3498],{"className":3499,"style":656},[634],[568,3501,3503,3506,3509],{"className":3502},[619],[568,3504],{"className":3505,"style":2596},[623],[568,3507,2540],{"className":3508},[628],[568,3510,605],{"className":3511},[628,629],[559,3513,3515],{"id":3514},"typische-fehler","Typische Fehler",[857,3517,3518,3674,4062],{},[860,3519,3520,3521,2603,3579,3613,3614,759],{},"Auch das Vorzeichen des Realteils umkehren. ",[568,3522,3524,3546],{"className":3523},[571],[568,3525,3527],{"className":3526},[575],[577,3528,3529],{"xmlns":579},[581,3530,3531,3543],{},[584,3532,3533,3535,3537,3539,3541],{},[591,3534,1014],{},[587,3536,596],{},[591,3538,1014],{},[587,3540,602],{},[587,3542,605],{},[607,3544,3545],{"encoding":609},"-a - bi",[568,3547,3549,3570],{"className":3548,"ariaHidden":615},[614],[568,3550,3552,3555,3558,3561,3564,3567],{"className":3551},[619],[568,3553],{"className":3554,"style":649},[623],[568,3556,1014],{"className":3557},[628],[568,3559,596],{"className":3560},[628,629],[568,3562],{"className":3563,"style":656},[634],[568,3565,1014],{"className":3566},[660],[568,3568],{"className":3569,"style":656},[634],[568,3571,3573,3576],{"className":3572},[619],[568,3574],{"className":3575,"style":670},[623],[568,3577,674],{"className":3578},[628,629],[568,3580,3582,3598],{"className":3581},[571],[568,3583,3585],{"className":3584},[575],[577,3586,3587],{"xmlns":579},[581,3588,3589,3595],{},[584,3590,3591,3593],{},[591,3592,1014],{},[587,3594,589],{},[607,3596,3597],{"encoding":609},"-z",[568,3599,3601],{"className":3600,"ariaHidden":615},[614],[568,3602,3604,3607,3610],{"className":3603},[619],[568,3605],{"className":3606,"style":649},[623],[568,3608,1014],{"className":3609},[628],[568,3611,589],{"className":3612,"style":630},[628,629],", nicht ",[568,3615,3617,3634],{"className":3616},[571],[568,3618,3620],{"className":3619},[575],[577,3621,3622],{"xmlns":579},[581,3623,3624,3632],{},[584,3625,3626],{},[694,3627,3628,3630],{"accent":615},[587,3629,589],{},[591,3631,700],{"stretchy":615},[607,3633,703],{"encoding":609},[568,3635,3637],{"className":3636,"ariaHidden":615},[614],[568,3638,3640,3643],{"className":3639},[619],[568,3641],{"className":3642,"style":713},[623],[568,3644,3646],{"className":3645},[628,717],[568,3647,3649],{"className":3648},[721],[568,3650,3652],{"className":3651},[725],[568,3653,3655,3666],{"className":3654,"style":713},[729],[568,3656,3657,3660],{"style":732},[568,3658],{"className":3659,"style":737},[736],[568,3661,3663],{"className":3662},[628],[568,3664,589],{"className":3665,"style":630},[628,629],[568,3667,3668,3671],{"style":746},[568,3669],{"className":3670,"style":737},[736],[568,3672],{"className":3673,"style":754},[753],[860,3675,3676,3677,3762,3763,3950,3951,759],{},"Beim Produkt ",[568,3678,3680,3703],{"className":3679},[571],[568,3681,3683],{"className":3682},[575],[577,3684,3685],{"xmlns":579},[581,3686,3687,3701],{},[584,3688,3689,3695,3697,3699],{},[1922,3690,3691,3693],{},[587,3692,605],{},[887,3694,889],{},[591,3696,593],{},[591,3698,1014],{},[887,3700,2449],{},[607,3702,2452],{"encoding":609},[568,3704,3706,3750],{"className":3705,"ariaHidden":615},[614],[568,3707,3709,3712,3741,3744,3747],{"className":3708},[619],[568,3710],{"className":3711,"style":2462},[623],[568,3713,3715,3718],{"className":3714},[628],[568,3716,605],{"className":3717},[628,629],[568,3719,3721],{"className":3720},[2138],[568,3722,3724],{"className":3723},[721],[568,3725,3727],{"className":3726},[725],[568,3728,3730],{"className":3729,"style":2462},[729],[568,3731,3732,3735],{"style":2483},[568,3733],{"className":3734,"style":2155},[736],[568,3736,3738],{"className":3737},[2159,2160,2161,2162],[568,3739,889],{"className":3740},[628,2162],[568,3742],{"className":3743,"style":635},[634],[568,3745,593],{"className":3746},[639],[568,3748],{"className":3749,"style":635},[634],[568,3751,3753,3756,3759],{"className":3752},[619],[568,3754],{"className":3755,"style":2508},[623],[568,3757,1014],{"className":3758},[628],[568,3760,2449],{"className":3761},[628]," vergessen und ",[568,3764,3766,3804],{"className":3765},[571],[568,3767,3769],{"className":3768},[575],[577,3770,3771],{"xmlns":579},[581,3772,3773,3801],{},[584,3774,3775,3777,3779,3785,3787,3793,3795],{},[587,3776,589],{},[591,3778,779],{},[694,3780,3781,3783],{"accent":615},[587,3782,589],{},[591,3784,700],{"stretchy":615},[591,3786,593],{},[1922,3788,3789,3791],{},[587,3790,596],{},[887,3792,889],{},[591,3794,1014],{},[1922,3796,3797,3799],{},[587,3798,602],{},[887,3800,889],{},[607,3802,3803],{"encoding":609},"z \\cdot \\overline{z} = a^2 - b^2",[568,3805,3807,3825,3871,3915],{"className":3806,"ariaHidden":615},[614],[568,3808,3810,3813,3816,3819,3822],{"className":3809},[619],[568,3811],{"className":3812,"style":798},[623],[568,3814,589],{"className":3815,"style":630},[628,629],[568,3817],{"className":3818,"style":656},[634],[568,3820,779],{"className":3821},[660],[568,3823],{"className":3824,"style":656},[634],[568,3826,3828,3831,3862,3865,3868],{"className":3827},[619],[568,3829],{"className":3830,"style":713},[623],[568,3832,3834],{"className":3833},[628,717],[568,3835,3837],{"className":3836},[721],[568,3838,3840],{"className":3839},[725],[568,3841,3843,3854],{"className":3842,"style":713},[729],[568,3844,3845,3848],{"style":732},[568,3846],{"className":3847,"style":737},[736],[568,3849,3851],{"className":3850},[628],[568,3852,589],{"className":3853,"style":630},[628,629],[568,3855,3856,3859],{"style":746},[568,3857],{"className":3858,"style":737},[736],[568,3860],{"className":3861,"style":754},[753],[568,3863],{"className":3864,"style":635},[634],[568,3866,593],{"className":3867},[639],[568,3869],{"className":3870,"style":635},[634],[568,3872,3874,3877,3906,3909,3912],{"className":3873},[619],[568,3875],{"className":3876,"style":3284},[623],[568,3878,3880,3883],{"className":3879},[628],[568,3881,596],{"className":3882},[628,629],[568,3884,3886],{"className":3885},[2138],[568,3887,3889],{"className":3888},[721],[568,3890,3892],{"className":3891},[725],[568,3893,3895],{"className":3894,"style":2462},[729],[568,3896,3897,3900],{"style":2483},[568,3898],{"className":3899,"style":2155},[736],[568,3901,3903],{"className":3902},[2159,2160,2161,2162],[568,3904,889],{"className":3905},[628,2162],[568,3907],{"className":3908,"style":656},[634],[568,3910,1014],{"className":3911},[660],[568,3913],{"className":3914,"style":656},[634],[568,3916,3918,3921],{"className":3917},[619],[568,3919],{"className":3920,"style":2462},[623],[568,3922,3924,3927],{"className":3923},[628],[568,3925,602],{"className":3926},[628,629],[568,3928,3930],{"className":3929},[2138],[568,3931,3933],{"className":3932},[721],[568,3934,3936],{"className":3935},[725],[568,3937,3939],{"className":3938,"style":2462},[729],[568,3940,3941,3944],{"style":2483},[568,3942],{"className":3943,"style":2155},[736],[568,3945,3947],{"className":3946},[2159,2160,2161,2162],[568,3948,889],{"className":3949},[628,2162]," rechnen. Richtig ist ",[568,3952,3954,3980],{"className":3953},[571],[568,3955,3957],{"className":3956},[575],[577,3958,3959],{"xmlns":579},[581,3960,3961,3977],{},[584,3962,3963,3969,3971],{},[1922,3964,3965,3967],{},[587,3966,596],{},[887,3968,889],{},[591,3970,599],{},[1922,3972,3973,3975],{},[587,3974,602],{},[887,3976,889],{},[607,3978,3979],{"encoding":609},"a^2 + b^2",[568,3981,3983,4027],{"className":3982,"ariaHidden":615},[614],[568,3984,3986,3989,4018,4021,4024],{"className":3985},[619],[568,3987],{"className":3988,"style":3284},[623],[568,3990,3992,3995],{"className":3991},[628],[568,3993,596],{"className":3994},[628,629],[568,3996,3998],{"className":3997},[2138],[568,3999,4001],{"className":4000},[721],[568,4002,4004],{"className":4003},[725],[568,4005,4007],{"className":4006,"style":2462},[729],[568,4008,4009,4012],{"style":2483},[568,4010],{"className":4011,"style":2155},[736],[568,4013,4015],{"className":4014},[2159,2160,2161,2162],[568,4016,889],{"className":4017},[628,2162],[568,4019],{"className":4020,"style":656},[634],[568,4022,599],{"className":4023},[660],[568,4025],{"className":4026,"style":656},[634],[568,4028,4030,4033],{"className":4029},[619],[568,4031],{"className":4032,"style":2462},[623],[568,4034,4036,4039],{"className":4035},[628],[568,4037,602],{"className":4038},[628,629],[568,4040,4042],{"className":4041},[2138],[568,4043,4045],{"className":4044},[721],[568,4046,4048],{"className":4047},[725],[568,4049,4051],{"className":4050,"style":2462},[729],[568,4052,4053,4056],{"style":2483},[568,4054],{"className":4055,"style":2155},[736],[568,4057,4059],{"className":4058},[2159,2160,2161,2162],[568,4060,889],{"className":4061},[628,2162],[860,4063,4064,4146,4147,4206,4207,4360,4361,759],{},[568,4065,4067,4088],{"className":4066},[571],[568,4068,4070],{"className":4069},[575],[577,4071,4072],{"xmlns":579},[581,4073,4074,4086],{},[584,4075,4076,4078,4080],{},[587,4077,589],{},[591,4079,779],{},[694,4081,4082,4084],{"accent":615},[587,4083,589],{},[591,4085,700],{"stretchy":615},[607,4087,788],{"encoding":609},[568,4089,4091,4109],{"className":4090,"ariaHidden":615},[614],[568,4092,4094,4097,4100,4103,4106],{"className":4093},[619],[568,4095],{"className":4096,"style":798},[623],[568,4098,589],{"className":4099,"style":630},[628,629],[568,4101],{"className":4102,"style":656},[634],[568,4104,779],{"className":4105},[660],[568,4107],{"className":4108,"style":656},[634],[568,4110,4112,4115],{"className":4111},[619],[568,4113],{"className":4114,"style":713},[623],[568,4116,4118],{"className":4117},[628,717],[568,4119,4121],{"className":4120},[721],[568,4122,4124],{"className":4123},[725],[568,4125,4127,4138],{"className":4126,"style":713},[729],[568,4128,4129,4132],{"style":732},[568,4130],{"className":4131,"style":737},[736],[568,4133,4135],{"className":4134},[628],[568,4136,589],{"className":4137,"style":630},[628,629],[568,4139,4140,4143],{"style":746},[568,4141],{"className":4142,"style":737},[736],[568,4144],{"className":4145,"style":754},[753]," mit ",[568,4148,4150,4168],{"className":4149},[571],[568,4151,4153],{"className":4152},[575],[577,4154,4155],{"xmlns":579},[581,4156,4157,4165],{},[584,4158,4159],{},[1922,4160,4161,4163],{},[587,4162,589],{},[887,4164,889],{},[607,4166,4167],{"encoding":609},"z^2",[568,4169,4171],{"className":4170,"ariaHidden":615},[614],[568,4172,4174,4177],{"className":4173},[619],[568,4175],{"className":4176,"style":2462},[623],[568,4178,4180,4183],{"className":4179},[628],[568,4181,589],{"className":4182,"style":630},[628,629],[568,4184,4186],{"className":4185},[2138],[568,4187,4189],{"className":4188},[721],[568,4190,4192],{"className":4191},[725],[568,4193,4195],{"className":4194,"style":2462},[729],[568,4196,4197,4200],{"style":2483},[568,4198],{"className":4199,"style":2155},[736],[568,4201,4203],{"className":4202},[2159,2160,2161,2162],[568,4204,889],{"className":4205},[628,2162]," verwechseln: ",[568,4208,4210,4252],{"className":4209},[571],[568,4211,4213],{"className":4212},[575],[577,4214,4215],{"xmlns":579},[581,4216,4217,4249],{},[584,4218,4219,4221,4223,4225,4227,4229,4235,4237,4239,4242,4244,4247],{},[591,4220,1895],{"stretchy":1894},[887,4222,2540],{},[591,4224,599],{},[887,4226,2545],{},[587,4228,605],{},[1922,4230,4231,4233],{},[591,4232,1906],{"stretchy":1894},[887,4234,889],{},[591,4236,593],{},[591,4238,1014],{},[887,4240,4241],{},"7",[591,4243,599],{},[887,4245,4246],{},"24",[587,4248,605],{},[607,4250,4251],{"encoding":609},"(3 + 4i)^2 = -7 + 24i",[568,4253,4255,4276,4327,4348],{"className":4254,"ariaHidden":615},[614],[568,4256,4258,4261,4264,4267,4270,4273],{"className":4257},[619],[568,4259],{"className":4260,"style":2056},[623],[568,4262,1895],{"className":4263},[2060],[568,4265,2540],{"className":4266},[628],[568,4268],{"className":4269,"style":656},[634],[568,4271,599],{"className":4272},[660],[568,4274],{"className":4275,"style":656},[634],[568,4277,4279,4283,4286,4289,4318,4321,4324],{"className":4278},[619],[568,4280],{"className":4281,"style":4282},[623],"height:1.0641em;vertical-align:-0.25em;",[568,4284,2545],{"className":4285},[628],[568,4287,605],{"className":4288},[628,629],[568,4290,4292,4295],{"className":4291},[2085],[568,4293,1906],{"className":4294},[2085],[568,4296,4298],{"className":4297},[2138],[568,4299,4301],{"className":4300},[721],[568,4302,4304],{"className":4303},[725],[568,4305,4307],{"className":4306,"style":2462},[729],[568,4308,4309,4312],{"style":2483},[568,4310],{"className":4311,"style":2155},[736],[568,4313,4315],{"className":4314},[2159,2160,2161,2162],[568,4316,889],{"className":4317},[628,2162],[568,4319],{"className":4320,"style":635},[634],[568,4322,593],{"className":4323},[639],[568,4325],{"className":4326,"style":635},[634],[568,4328,4330,4333,4336,4339,4342,4345],{"className":4329},[619],[568,4331],{"className":4332,"style":2508},[623],[568,4334,1014],{"className":4335},[628],[568,4337,4241],{"className":4338},[628],[568,4340],{"className":4341,"style":656},[634],[568,4343,599],{"className":4344},[660],[568,4346],{"className":4347,"style":656},[634],[568,4349,4351,4354,4357],{"className":4350},[619],[568,4352],{"className":4353,"style":2596},[623],[568,4355,4246],{"className":4356},[628],[568,4358,605],{"className":4359},[628,629],", aber ",[568,4362,4364,4404],{"className":4363},[571],[568,4365,4367],{"className":4366},[575],[577,4368,4369],{"xmlns":579},[581,4370,4371,4401],{},[584,4372,4373,4375,4377,4379,4381,4383,4385,4387,4389,4391,4393,4395,4397,4399],{},[591,4374,1895],{"stretchy":1894},[887,4376,2540],{},[591,4378,599],{},[887,4380,2545],{},[587,4382,605],{},[591,4384,1906],{"stretchy":1894},[591,4386,1895],{"stretchy":1894},[887,4388,2540],{},[591,4390,1014],{},[887,4392,2545],{},[587,4394,605],{},[591,4396,1906],{"stretchy":1894},[591,4398,593],{},[887,4400,2754],{},[607,4402,4403],{"encoding":609},"(3 + 4i)(3 - 4i) = 25",[568,4405,4407,4428,4458,4482],{"className":4406,"ariaHidden":615},[614],[568,4408,4410,4413,4416,4419,4422,4425],{"className":4409},[619],[568,4411],{"className":4412,"style":2056},[623],[568,4414,1895],{"className":4415},[2060],[568,4417,2540],{"className":4418},[628],[568,4420],{"className":4421,"style":656},[634],[568,4423,599],{"className":4424},[660],[568,4426],{"className":4427,"style":656},[634],[568,4429,4431,4434,4437,4440,4443,4446,4449,4452,4455],{"className":4430},[619],[568,4432],{"className":4433,"style":2056},[623],[568,4435,2545],{"className":4436},[628],[568,4438,605],{"className":4439},[628,629],[568,4441,1906],{"className":4442},[2085],[568,4444,1895],{"className":4445},[2060],[568,4447,2540],{"className":4448},[628],[568,4450],{"className":4451,"style":656},[634],[568,4453,1014],{"className":4454},[660],[568,4456],{"className":4457,"style":656},[634],[568,4459,4461,4464,4467,4470,4473,4476,4479],{"className":4460},[619],[568,4462],{"className":4463,"style":2056},[623],[568,4465,2545],{"className":4466},[628],[568,4468,605],{"className":4469},[628,629],[568,4471,1906],{"className":4472},[2085],[568,4474],{"className":4475,"style":635},[634],[568,4477,593],{"className":4478},[639],[568,4480],{"className":4481,"style":635},[634],[568,4483,4485,4488],{"className":4484},[619],[568,4486],{"className":4487,"style":2883},[623],[568,4489,2754],{"className":4490},[628],{"title":4492,"searchDepth":4493,"depth":4493,"links":4494},"",2,[4495,4496,4497,4498],{"id":561,"depth":4493,"text":562},{"id":1861,"depth":4493,"text":1862},{"id":2517,"depth":4493,"text":2518},{"id":3514,"depth":4493,"text":3515},[4500,4502,4505,4507,4509,4512,4515,4518,4520,4522,4524,4526,4528,4531,4533,4535,4537,4539,4542],{"lhs":4501,"rhs":596},"re(conj(complex(a, b)))",{"lhs":4503,"rhs":4504},"im(conj(complex(a, b)))","-b",{"lhs":4506,"rhs":3979},"re(complex(a, b) * conj(complex(a, b)))",{"lhs":4508,"rhs":3271},"im(complex(a, b) * conj(complex(a, b)))",{"lhs":4510,"rhs":4511},"re(conj(complex(a, b) * complex(c, d)))","re(conj(complex(a, b)) * conj(complex(c, d)))",{"lhs":4513,"rhs":4514},"im(conj(complex(a, b) * complex(c, d)))","im(conj(complex(a, b)) * conj(complex(c, d)))",{"lhs":4516,"rhs":4517},"im(conj(3 + 4*i))","-4",{"lhs":4519,"rhs":2754},"re((3 + 4*i) * (3 - 4*i))",{"lhs":4521,"rhs":3271},"im((3 + 4*i) * (3 - 4*i))",{"lhs":4523,"rhs":2788},"re((3 + 4*i) + (3 - 4*i))",{"lhs":4525,"rhs":3271},"im((3 + 4*i) + (3 - 4*i))",{"lhs":4527,"rhs":3059},"im(conj(-2 - 5*i))",{"lhs":4529,"rhs":4530},"re(conj(-2 - 5*i))","-2",{"lhs":4532,"rhs":3271},"re((2 + 3*i)^2 - 4*(2 + 3*i) + 13)",{"lhs":4534,"rhs":3271},"im((2 + 3*i)^2 - 4*(2 + 3*i) + 13)",{"lhs":4536,"rhs":3271},"re((2 - 3*i)^2 - 4*(2 - 3*i) + 13)",{"lhs":4538,"rhs":3271},"im((2 - 3*i)^2 - 4*(2 - 3*i) + 13)",{"lhs":4540,"rhs":4541},"re((3 + 4*i)^2)","-7",{"lhs":4543,"rhs":4246},"im((3 + 4*i)^2)","z = a + bi,\\ a, b \\in \\mathbb{R}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>z\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">z = a + 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 class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">bi\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>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b \\in \\mathbb{R}\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\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:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","complex-conjugate","\\overline{z} = a - bi, \\qquad z \\cdot \\overline{z} = a^2 + b^2 = |z|^2","\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>\u003Cmover accent=\"true\">\u003Cmi>z\u003C\u002Fmi>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmi>z\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>z\u003C\u002Fmi>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmi>z\u003C\u002Fmi>\u003Cmsup>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\overline{z} = a - bi, \\qquad z \\cdot \\overline{z} = a^2 + b^2 = |z|^2\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:0.6306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord 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style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":596,"meaning":4577,"symbolHtml":4578},"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 class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":602,"meaning":4580,"symbolHtml":4581},"Imaginärteil von z","\u003Cspan class=\"katex\">\u003Cspan 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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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.044em;\">z\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","g7HyFaeQfP0ho17wgys3c2bJI1LkJSVgxULlGiUhii0",[4588,4591,4594],{"stem":4589,"title":4590,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fbetrag-komplexe-zahl","Betrag einer komplexen Zahl",{"stem":4592,"title":4593,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fdivision-komplexer-zahlen","Division komplexer Zahlen",{"stem":4595,"title":4596,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fkomplexe-zahl","Komplexe Zahl in algebraischer Form",1793824272226]