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Beide sind reelle Zahlen.",[951,1100,1101,1102,957,1155,1183,1184,1235,1236,1329,1330,1358],{},"Für ",[570,1103,1105,1124],{"className":1104},[573],[570,1106,1108],{"className":1107},[577],[579,1109,1110],{"xmlns":581},[583,1111,1112,1121],{},[586,1113,1114,1116,1118],{},[592,1115,851],{},[600,1117,602],{},[596,1119,1120],{},"0",[610,1122,1123],{"encoding":612},"b = 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",[570,1185,1187,1205],{"className":1186},[573],[570,1188,1190],{"className":1189},[577],[579,1191,1192],{"xmlns":581},[583,1193,1194,1202],{},[586,1195,1196,1198,1200],{},[592,1197,845],{},[600,1199,602],{},[596,1201,1120],{},[610,1203,1204],{"encoding":612},"a = 0",[570,1206,1208,1226],{"className":1207,"ariaHidden":618},[617],[570,1209,1211,1214,1217,1220,1223],{"className":1210},[622],[570,1212],{"className":1213,"style":866},[626],[570,1215,845],{"className":1216},[631,635],[570,1218],{"className":1219,"style":674},[673],[570,1221,602],{"className":1222},[678],[570,1224],{"className":1225,"style":674},[673],[570,1227,1229,1232],{"className":1228},[622],[570,1230],{"className":1231,"style":1151},[626],[570,1233,1120],{"className":1234},[631]," und ",[570,1237,1239,1258],{"className":1238},[573],[570,1240,1242],{"className":1241},[577],[579,1243,1244],{"xmlns":581},[583,1245,1246,1255],{},[586,1247,1248,1250,1253],{},[592,1249,851],{},[600,1251,1252],{"mathvariant":972},"≠",[596,1254,1120],{},[610,1256,1257],{"encoding":612},"b \\neq 0",[570,1259,1261,1320],{"className":1260,"ariaHidden":618},[617],[570,1262,1264,1268,1271,1274,1317],{"className":1263},[622],[570,1265],{"className":1266,"style":1267},[626],"height:0.8889em;vertical-align:-0.1944em;",[570,1269,851],{"className":1270},[631,635],[570,1272],{"className":1273,"style":674},[673],[570,1275,1277,1310,1314],{"className":1276},[678],[570,1278,1280],{"className":1279},[678],[570,1281,1284],{"className":1282},[631,1283],"vbox",[570,1285,1288],{"className":1286},[1287],"thinbox",[570,1289,1292,1295,1306],{"className":1290},[1291],"rlap",[570,1293],{"className":1294,"style":1267},[626],[570,1296,1299],{"className":1297},[1298],"inner",[570,1300,1302],{"className":1301},[631],[570,1303,1305],{"className":1304},[678],"",[570,1307],{"className":1308},[1309],"fix",[570,1311],{"className":1312},[673,1313],"nobreak",[570,1315,602],{"className":1316},[678],[570,1318],{"className":1319,"style":674},[673],[570,1321,1323,1326],{"className":1322},[622],[570,1324],{"className":1325,"style":1151},[626],[570,1327,1120],{"className":1328},[631]," heißt ",[570,1331,1333,1346],{"className":1332},[573],[570,1334,1336],{"className":1335},[577],[579,1337,1338],{"xmlns":581},[583,1339,1340,1344],{},[586,1341,1342],{},[592,1343,840],{},[610,1345,840],{"encoding":612},[570,1347,1349],{"className":1348,"ariaHidden":618},[617],[570,1350,1352,1355],{"className":1351},[622],[570,1353],{"className":1354,"style":866},[626],[570,1356,840],{"className":1357,"style":870},[631,635]," rein imaginär.",[951,1360,1361],{},"Zwei komplexe Zahlen sind gleich, wenn Realteile und Imaginärteile übereinstimmen.",[566,1363,1364,1365,1368,1369,1443,1444,1512],{},"In der ",[697,1366,1367],{},"Gaußschen Zahlenebene"," stellt man ",[570,1370,1372,1395],{"className":1371},[573],[570,1373,1375],{"className":1374},[577],[579,1376,1377],{"xmlns":581},[583,1378,1379,1393],{},[586,1380,1381,1383,1385,1387,1389,1391],{},[592,1382,840],{},[600,1384,602],{},[592,1386,845],{},[600,1388,848],{},[592,1390,851],{},[592,1392,718],{},[610,1394,856],{"encoding":612},[570,1396,1398,1416,1434],{"className":1397,"ariaHidden":618},[617],[570,1399,1401,1404,1407,1410,1413],{"className":1400},[622],[570,1402],{"className":1403,"style":866},[626],[570,1405,840],{"className":1406,"style":870},[631,635],[570,1408],{"className":1409,"style":674},[673],[570,1411,602],{"className":1412},[678],[570,1414],{"className":1415,"style":674},[673],[570,1417,1419,1422,1425,1428,1431],{"className":1418},[622],[570,1420],{"className":1421,"style":886},[626],[570,1423,845],{"className":1424},[631,635],[570,1426],{"className":1427,"style":893},[673],[570,1429,848],{"className":1430},[897],[570,1432],{"className":1433,"style":893},[673],[570,1435,1437,1440],{"className":1436},[622],[570,1438],{"className":1439,"style":907},[626],[570,1441,911],{"className":1442},[631,635]," als Punkt ",[570,1445,1447,1473],{"className":1446},[573],[570,1448,1450],{"className":1449},[577],[579,1451,1452],{"xmlns":581},[583,1453,1454,1470],{},[586,1455,1456,1460,1462,1465,1467],{},[600,1457,1459],{"stretchy":1458},"false","(",[592,1461,845],{},[600,1463,1464],{},"∣",[592,1466,851],{},[600,1468,1469],{"stretchy":1458},")",[610,1471,1472],{"encoding":612},"(a \\mid b)",[570,1474,1476,1499],{"className":1475,"ariaHidden":618},[617],[570,1477,1479,1483,1487,1490,1493,1496],{"className":1478},[622],[570,1480],{"className":1481,"style":1482},[626],"height:1em;vertical-align:-0.25em;",[570,1484,1459],{"className":1485},[1486],"mopen",[570,1488,845],{"className":1489},[631,635],[570,1491],{"className":1492,"style":674},[673],[570,1494,1464],{"className":1495},[678],[570,1497],{"className":1498,"style":674},[673],[570,1500,1502,1505,1508],{"className":1501},[622],[570,1503],{"className":1504,"style":1482},[626],[570,1506,851],{"className":1507},[631,635],[570,1509,1469],{"className":1510},[1511],"mclose"," dar: Realteil nach rechts, Imaginärteil nach oben.",[566,1514,1515,1516,1575,1576,1610,1611,1639,1640,1669],{},"Gerechnet wird wie mit Termen, wobei man ",[570,1517,1519,1537],{"className":1518},[573],[570,1520,1522],{"className":1521},[577],[579,1523,1524],{"xmlns":581},[583,1525,1526,1534],{},[586,1527,1528],{},[589,1529,1530,1532],{},[592,1531,718],{},[596,1533,598],{},[610,1535,1536],{"encoding":612},"i^2",[570,1538,1540],{"className":1539,"ariaHidden":618},[617],[570,1541,1543,1546],{"className":1542},[622],[570,1544],{"className":1545,"style":627},[626],[570,1547,1549,1552],{"className":1548},[631],[570,1550,718],{"className":1551},[631,635],[570,1553,1555],{"className":1554},[639],[570,1556,1558],{"className":1557},[643],[570,1559,1561],{"className":1560},[647],[570,1562,1564],{"className":1563,"style":627},[651],[570,1565,1566,1569],{"style":654},[570,1567],{"className":1568,"style":659},[658],[570,1570,1572],{"className":1571},[663,664,665,666],[570,1573,598],{"className":1574},[631,666]," durch ",[570,1577,1579,1595],{"className":1578},[573],[570,1580,1582],{"className":1581},[577],[579,1583,1584],{"xmlns":581},[583,1585,1586,1592],{},[586,1587,1588,1590],{},[600,1589,605],{},[596,1591,608],{},[610,1593,1594],{"encoding":612},"-1",[570,1596,1598],{"className":1597,"ariaHidden":618},[617],[570,1599,1601,1604,1607],{"className":1600},[622],[570,1602],{"className":1603,"style":688},[626],[570,1605,605],{"className":1606},[631],[570,1608,608],{"className":1609},[631]," ersetzt. Addition und Subtraktion erfolgen getrennt nach Real- und Imaginärteil. Die Potenzen von ",[570,1612,1614,1627],{"className":1613},[573],[570,1615,1617],{"className":1616},[577],[579,1618,1619],{"xmlns":581},[583,1620,1621,1625],{},[586,1622,1623],{},[592,1624,718],{},[610,1626,718],{"encoding":612},[570,1628,1630],{"className":1629,"ariaHidden":618},[617],[570,1631,1633,1636],{"className":1632},[622],[570,1634],{"className":1635,"style":730},[626],[570,1637,718],{"className":1638},[631,635]," wiederholen sich mit der Periode ",[570,1641,1643,1657],{"className":1642},[573],[570,1644,1646],{"className":1645},[577],[579,1647,1648],{"xmlns":581},[583,1649,1650,1655],{},[586,1651,1652],{},[596,1653,1654],{},"4",[610,1656,1654],{"encoding":612},[570,1658,1660],{"className":1659,"ariaHidden":618},[617],[570,1661,1663,1666],{"className":1662},[622],[570,1664],{"className":1665,"style":1151},[626],[570,1667,1654],{"className":1668},[631],":",[570,1671,1674],{"className":1672},[1673],"katex-display",[570,1675,1677,1749],{"className":1676},[573],[570,1678,1680],{"className":1679},[577],[579,1681,1683],{"xmlns":581,"display":1682},"block",[583,1684,1685,1746],{},[586,1686,1687,1693,1695,1697,1700,1703,1709,1711,1713,1715,1717,1719,1726,1728,1730,1732,1734,1736,1742,1744],{},[589,1688,1689,1691],{},[592,1690,718],{},[596,1692,608],{},[600,1694,602],{},[592,1696,718],{},[600,1698,1699],{"separator":618},",",[673,1701],{"width":1702},"1em",[589,1704,1705,1707],{},[592,1706,718],{},[596,1708,598],{},[600,1710,602],{},[600,1712,605],{},[596,1714,608],{},[600,1716,1699],{"separator":618},[673,1718],{"width":1702},[589,1720,1721,1723],{},[592,1722,718],{},[596,1724,1725],{},"3",[600,1727,602],{},[600,1729,605],{},[592,1731,718],{},[600,1733,1699],{"separator":618},[673,1735],{"width":1702},[589,1737,1738,1740],{},[592,1739,718],{},[596,1741,1654],{},[600,1743,602],{},[596,1745,608],{},[610,1747,1748],{"encoding":612},"i^1 = i, \\quad i^2 = -1, \\quad i^3 = -i, \\quad i^4 = 1",[570,1750,1752,1798,1857,1916,1975],{"className":1751,"ariaHidden":618},[617],[570,1753,1755,1759,1789,1792,1795],{"className":1754},[622],[570,1756],{"className":1757,"style":1758},[626],"height:0.8641em;",[570,1760,1762,1765],{"className":1761},[631],[570,1763,718],{"className":1764},[631,635],[570,1766,1768],{"className":1767},[639],[570,1769,1771],{"className":1770},[643],[570,1772,1774],{"className":1773},[647],[570,1775,1777],{"className":1776,"style":1758},[651],[570,1778,1780,1783],{"style":1779},"top:-3.113em;margin-right:0.05em;",[570,1781],{"className":1782,"style":659},[658],[570,1784,1786],{"className":1785},[663,664,665,666],[570,1787,608],{"className":1788},[631,666],[570,1790],{"className":1791,"style":674},[673],[570,1793,602],{"className":1794},[678],[570,1796],{"className":1797,"style":674},[673],[570,1799,1801,1805,1808,1812,1816,1819,1848,1851,1854],{"className":1800},[622],[570,1802],{"className":1803,"style":1804},[626],"height:1.0585em;vertical-align:-0.1944em;",[570,1806,718],{"className":1807},[631,635],[570,1809,1699],{"className":1810},[1811],"mpunct",[570,1813],{"className":1814,"style":1815},[673],"margin-right:1em;",[570,1817],{"className":1818,"style":1007},[673],[570,1820,1822,1825],{"className":1821},[631],[570,1823,718],{"className":1824},[631,635],[570,1826,1828],{"className":1827},[639],[570,1829,1831],{"className":1830},[643],[570,1832,1834],{"className":1833},[647],[570,1835,1837],{"className":1836,"style":1758},[651],[570,1838,1839,1842],{"style":1779},[570,1840],{"className":1841,"style":659},[658],[570,1843,1845],{"className":1844},[663,664,665,666],[570,1846,598],{"className":1847},[631,666],[570,1849],{"className":1850,"style":674},[673],[570,1852,602],{"className":1853},[678],[570,1855],{"className":1856,"style":674},[673],[570,1858,1860,1863,1866,1869,1872,1875,1878,1907,1910,1913],{"className":1859},[622],[570,1861],{"className":1862,"style":1804},[626],[570,1864,605],{"className":1865},[631],[570,1867,608],{"className":1868},[631],[570,1870,1699],{"className":1871},[1811],[570,1873],{"className":1874,"style":1815},[673],[570,1876],{"className":1877,"style":1007},[673],[570,1879,1881,1884],{"className":1880},[631],[570,1882,718],{"className":1883},[631,635],[570,1885,1887],{"className":1886},[639],[570,1888,1890],{"className":1889},[643],[570,1891,1893],{"className":1892},[647],[570,1894,1896],{"className":1895,"style":1758},[651],[570,1897,1898,1901],{"style":1779},[570,1899],{"className":1900,"style":659},[658],[570,1902,1904],{"className":1903},[663,664,665,666],[570,1905,1725],{"className":1906},[631,666],[570,1908],{"className":1909,"style":674},[673],[570,1911,602],{"className":1912},[678],[570,1914],{"className":1915,"style":674},[673],[570,1917,1919,1922,1925,1928,1931,1934,1937,1966,1969,1972],{"className":1918},[622],[570,1920],{"className":1921,"style":1804},[626],[570,1923,605],{"className":1924},[631],[570,1926,718],{"className":1927},[631,635],[570,1929,1699],{"className":1930},[1811],[570,1932],{"className":1933,"style":1815},[673],[570,1935],{"className":1936,"style":1007},[673],[570,1938,1940,1943],{"className":1939},[631],[570,1941,718],{"className":1942},[631,635],[570,1944,1946],{"className":1945},[639],[570,1947,1949],{"className":1948},[643],[570,1950,1952],{"className":1951},[647],[570,1953,1955],{"className":1954,"style":1758},[651],[570,1956,1957,1960],{"style":1779},[570,1958],{"className":1959,"style":659},[658],[570,1961,1963],{"className":1962},[663,664,665,666],[570,1964,1654],{"className":1965},[631,666],[570,1967],{"className":1968,"style":674},[673],[570,1970,602],{"className":1971},[678],[570,1973],{"className":1974,"style":674},[673],[570,1976,1978,1981],{"className":1977},[622],[570,1979],{"className":1980,"style":1151},[626],[570,1982,608],{"className":1983},[631],[561,1985,1987],{"id":1986},"beispiele","Beispiele",[570,1989,1991],{"className":1990},[1673],[570,1992,1994,2043],{"className":1993},[573],[570,1995,1997],{"className":1996},[577],[579,1998,1999],{"xmlns":581,"display":1682},[583,2000,2001,2040],{},[586,2002,2003,2005,2007,2009,2011,2013,2015,2017,2019,2021,2023,2026,2028,2030,2032,2034,2036,2038],{},[600,2004,1459],{"stretchy":1458},[596,2006,1725],{},[600,2008,848],{},[596,2010,598],{},[592,2012,718],{},[600,2014,1469],{"stretchy":1458},[600,2016,848],{},[600,2018,1459],{"stretchy":1458},[596,2020,608],{},[600,2022,605],{},[596,2024,2025],{},"5",[592,2027,718],{},[600,2029,1469],{"stretchy":1458},[600,2031,602],{},[596,2033,1654],{},[600,2035,605],{},[596,2037,1725],{},[592,2039,718],{},[610,2041,2042],{"encoding":612},"(3 + 2i) + (1 - 5i) = 4 - 3i",[570,2044,2046,2067,2091,2112,2136,2154],{"className":2045,"ariaHidden":618},[617],[570,2047,2049,2052,2055,2058,2061,2064],{"className":2048},[622],[570,2050],{"className":2051,"style":1482},[626],[570,2053,1459],{"className":2054},[1486],[570,2056,1725],{"className":2057},[631],[570,2059],{"className":2060,"style":893},[673],[570,2062,848],{"className":2063},[897],[570,2065],{"className":2066,"style":893},[673],[570,2068,2070,2073,2076,2079,2082,2085,2088],{"className":2069},[622],[570,2071],{"className":2072,"style":1482},[626],[570,2074,598],{"className":2075},[631],[570,2077,718],{"className":2078},[631,635],[570,2080,1469],{"className":2081},[1511],[570,2083],{"className":2084,"style":893},[673],[570,2086,848],{"className":2087},[897],[570,2089],{"className":2090,"style":893},[673],[570,2092,2094,2097,2100,2103,2106,2109],{"className":2093},[622],[570,2095],{"className":2096,"style":1482},[626],[570,2098,1459],{"className":2099},[1486],[570,2101,608],{"className":2102},[631],[570,2104],{"className":2105,"style":893},[673],[570,2107,605],{"className":2108},[897],[570,2110],{"className":2111,"style":893},[673],[570,2113,2115,2118,2121,2124,2127,2130,2133],{"className":2114},[622],[570,2116],{"className":2117,"style":1482},[626],[570,2119,2025],{"className":2120},[631],[570,2122,718],{"className":2123},[631,635],[570,2125,1469],{"className":2126},[1511],[570,2128],{"className":2129,"style":674},[673],[570,2131,602],{"className":2132},[678],[570,2134],{"className":2135,"style":674},[673],[570,2137,2139,2142,2145,2148,2151],{"className":2138},[622],[570,2140],{"className":2141,"style":688},[626],[570,2143,1654],{"className":2144},[631],[570,2146],{"className":2147,"style":893},[673],[570,2149,605],{"className":2150},[897],[570,2152],{"className":2153,"style":893},[673],[570,2155,2157,2160,2163],{"className":2156},[622],[570,2158],{"className":2159,"style":730},[626],[570,2161,1725],{"className":2162},[631],[570,2164,718],{"className":2165},[631,635],[570,2167,2169],{"className":2168},[1673],[570,2170,2172,2228],{"className":2171},[573],[570,2173,2175],{"className":2174},[577],[579,2176,2177],{"xmlns":581,"display":1682},[583,2178,2179,2225],{},[586,2180,2181,2188,2190,2196,2199,2205,2207,2209,2211,2213,2215,2217,2219,2221,2223],{},[589,2182,2183,2185],{},[592,2184,718],{},[596,2186,2187],{},"7",[600,2189,602],{},[589,2191,2192,2194],{},[592,2193,718],{},[596,2195,1654],{},[600,2197,2198],{},"⋅",[589,2200,2201,2203],{},[592,2202,718],{},[596,2204,1725],{},[600,2206,602],{},[596,2208,608],{},[600,2210,2198],{},[600,2212,1459],{"stretchy":1458},[600,2214,605],{},[592,2216,718],{},[600,2218,1469],{"stretchy":1458},[600,2220,602],{},[600,2222,605],{},[592,2224,718],{},[610,2226,2227],{"encoding":612},"i^7 = i^4 \\cdot i^3 = 1 \\cdot (-i) = 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Gleichung mit negativer Diskriminante: ",[570,2425,2427,2459],{"className":2426},[573],[570,2428,2430],{"className":2429},[577],[579,2431,2432],{"xmlns":581},[583,2433,2434,2456],{},[586,2435,2436,2442,2444,2446,2448,2450,2452,2454],{},[589,2437,2438,2440],{},[592,2439,594],{},[596,2441,598],{},[600,2443,848],{},[596,2445,598],{},[592,2447,594],{},[600,2449,848],{},[596,2451,2025],{},[600,2453,602],{},[596,2455,1120],{},[610,2457,2458],{"encoding":612},"x^2 + 2x + 5 = 0",[570,2460,2462,2507,2528,2546],{"className":2461,"ariaHidden":618},[617],[570,2463,2465,2469,2498,2501,2504],{"className":2464},[622],[570,2466],{"className":2467,"style":2468},[626],"height:0.8974em;vertical-align:-0.0833em;",[570,2470,2472,2475],{"className":2471},[631],[570,2473,594],{"className":2474},[631,635],[570,2476,2478],{"className":2477},[639],[570,2479,2481],{"className":2480},[643],[570,2482,2484],{"className":2483},[647],[570,2485,2487],{"className":2486,"style":627},[651],[570,2488,2489,2492],{"style":654},[570,2490],{"className":2491,"style":659},[658],[570,2493,2495],{"className":2494},[663,664,665,666],[570,2496,598],{"className":2497},[631,666],[570,2499],{"className":2500,"style":893},[673],[570,2502,848],{"className":2503},[897],[570,2505],{"className":2506,"style":893},[673],[570,2508,2510,2513,2516,2519,2522,2525],{"className":2509},[622],[570,2511],{"className":2512,"style":688},[626],[570,2514,598],{"className":2515},[631],[570,2517,594],{"className":2518},[631,635],[570,2520],{"className":2521,"style":893},[673],[570,2523,848],{"className":2524},[897],[570,2526],{"className":2527,"style":893},[673],[570,2529,2531,2534,2537,2540,2543],{"className":2530},[622],[570,2532],{"className":2533,"style":1151},[626],[570,2535,2025],{"className":2536},[631],[570,2538],{"className":2539,"style":674},[673],[570,2541,602],{"className":2542},[678],[570,2544],{"className":2545,"style":674},[673],[570,2547,2549,2552],{"className":2548},[622],[570,2550],{"className":2551,"style":1151},[626],[570,2553,1120],{"className":2554},[631]," hat ",[570,2557,2559,2601],{"className":2558},[573],[570,2560,2562],{"className":2561},[577],[579,2563,2564],{"xmlns":581},[583,2565,2566,2598],{},[586,2567,2568,2571,2573,2579,2581,2583,2585,2587,2589,2591,2593,2595],{},[592,2569,2570],{},"D",[600,2572,602],{},[589,2574,2575,2577],{},[596,2576,598],{},[596,2578,598],{},[600,2580,605],{},[596,2582,1654],{},[600,2584,2198],{},[596,2586,608],{},[600,2588,2198],{},[596,2590,2025],{},[600,2592,602],{},[600,2594,605],{},[596,2596,2597],{},"16",[610,2599,2600],{"encoding":612},"D = 2^2 - 4 \\cdot 1 \\cdot 5 = 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abc-Formel",[570,2868,2870],{"className":2869},[1673],[570,2871,2873,2930],{"className":2872},[573],[570,2874,2876],{"className":2875},[577],[579,2877,2878],{"xmlns":581,"display":1682},[583,2879,2880,2927],{},[586,2881,2882,2895,2897,2915,2917,2919,2921,2923,2925],{},[2883,2884,2885,2887],"msub",{},[592,2886,594],{},[586,2888,2889,2891,2893],{},[596,2890,608],{},[600,2892,1699],{"separator":618},[596,2894,598],{},[600,2896,602],{},[2898,2899,2900,2913],"mfrac",{},[586,2901,2902,2904,2906,2909,2911],{},[600,2903,605],{},[596,2905,598],{},[600,2907,2908],{},"±",[596,2910,1654],{},[592,2912,718],{},[596,2914,598],{},[600,2916,602],{},[600,2918,605],{},[596,2920,608],{},[600,2922,2908],{},[596,2924,598],{},[592,2926,718],{},[610,2928,2929],{"encoding":612},"x_{1,2} = \\frac{-2 \\pm 4i}{2} = -1 \\pm 2i",[570,2931,2933,3001,3105,3126],{"className":2932,"ariaHidden":618},[617],[570,2934,2936,2940,2992,2995,2998],{"className":2935},[622],[570,2937],{"className":2938,"style":2939},[626],"height:0.7167em;vertical-align:-0.2861em;",[570,2941,2943,2946],{"className":2942},[631],[570,2944,594],{"className":2945},[631,635],[570,2947,2949],{"className":2948},[639],[570,2950,2952,2983],{"className":2951},[643,2781],[570,2953,2955,2980],{"className":2954},[647],[570,2956,2959],{"className":2957,"style":2958},[651],"height:0.3011em;",[570,2960,2962,2965],{"style":2961},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[570,2963],{"className":2964,"style":659},[658],[570,2966,2968],{"className":2967},[663,664,665,666],[570,2969,2971,2974,2977],{"className":2970},[631,666],[570,2972,608],{"className":2973},[631,666],[570,2975,1699],{"className":2976},[1811,666],[570,2978,598],{"className":2979},[631,666],[570,2981,2835],{"className":2982},[2834],[570,2984,2986],{"className":2985},[647],[570,2987,2990],{"className":2988,"style":2989},[651],"height:0.2861em;",[570,2991],{},[570,2993],{"className":2994,"style":674},[673],[570,2996,602],{"className":2997},[678],[570,2999],{"className":3000,"style":674},[673],[570,3002,3004,3008,3096,3099,3102],{"className":3003},[622],[570,3005],{"className":3006,"style":3007},[626],"height:2.0225em;vertical-align:-0.686em;",[570,3009,3011,3015,3093],{"className":3010},[631],[570,3012],{"className":3013},[1486,3014],"nulldelimiter",[570,3016,3018],{"className":3017},[2898],[570,3019,3021,3084],{"className":3020},[643,2781],[570,3022,3024,3081],{"className":3023},[647],[570,3025,3028,3040,3051],{"className":3026,"style":3027},[651],"height:1.3365em;",[570,3029,3031,3034],{"style":3030},"top:-2.314em;",[570,3032],{"className":3033,"style":2797},[658],[570,3035,3037],{"className":3036},[631],[570,3038,598],{"className":3039},[631],[570,3041,3043,3046],{"style":3042},"top:-3.23em;",[570,3044],{"className":3045,"style":2797},[658],[570,3047],{"className":3048,"style":3050},[3049],"frac-line","border-bottom-width:0.04em;",[570,3052,3054,3057],{"style":3053},"top:-3.677em;",[570,3055],{"className":3056,"style":2797},[658],[570,3058,3060,3063,3066,3069,3072,3075,3078],{"className":3059},[631],[570,3061,605],{"className":3062},[631],[570,3064,598],{"className":3065},[631],[570,3067],{"className":3068,"style":893},[673],[570,3070,2908],{"className":3071},[897],[570,3073],{"className":3074,"style":893},[673],[570,3076,1654],{"className":3077},[631],[570,3079,718],{"className":3080},[631,635],[570,3082,2835],{"className":3083},[2834],[570,3085,3087],{"className":3086},[647],[570,3088,3091],{"className":3089,"style":3090},[651],"height:0.686em;",[570,3092],{},[570,3094],{"className":3095},[1511,3014],[570,3097],{"className":3098,"style":674},[673],[570,3100,602],{"className":3101},[678],[570,3103],{"className":3104,"style":674},[673],[570,3106,3108,3111,3114,3117,3120,3123],{"className":3107},[622],[570,3109],{"className":3110,"style":688},[626],[570,3112,605],{"className":3113},[631],[570,3115,608],{"className":3116},[631],[570,3118],{"className":3119,"style":893},[673],[570,3121,2908],{"className":3122},[897],[570,3124],{"className":3125,"style":893},[673],[570,3127,3129,3132,3135],{"className":3128},[622],[570,3130],{"className":3131,"style":730},[626],[570,3133,598],{"className":3134},[631],[570,3136,718],{"className":3137},[631,635],[561,3139,3141],{"id":3140},"typische-fehler","Typische Fehler",[948,3143,3144,3363,3800,3970],{},[951,3145,3146,3147,3175,3176,957,3254,3323,3324,946],{},"Den Imaginärteil mit ",[570,3148,3150,3163],{"className":3149},[573],[570,3151,3153],{"className":3152},[577],[579,3154,3155],{"xmlns":581},[583,3156,3157,3161],{},[586,3158,3159],{},[592,3160,718],{},[610,3162,718],{"encoding":612},[570,3164,3166],{"className":3165,"ariaHidden":618},[617],[570,3167,3169,3172],{"className":3168},[622],[570,3170],{"className":3171,"style":730},[626],[570,3173,718],{"className":3174},[631,635]," angeben: Für ",[570,3177,3179,3203],{"className":3178},[573],[570,3180,3182],{"className":3181},[577],[579,3183,3184],{"xmlns":581},[583,3185,3186,3200],{},[586,3187,3188,3190,3192,3194,3196,3198],{},[592,3189,840],{},[600,3191,602],{},[596,3193,1725],{},[600,3195,605],{},[596,3197,2025],{},[592,3199,718],{},[610,3201,3202],{"encoding":612},"z = 3 - 5i",[570,3204,3206,3224,3242],{"className":3205,"ariaHidden":618},[617],[570,3207,3209,3212,3215,3218,3221],{"className":3208},[622],[570,3210],{"className":3211,"style":866},[626],[570,3213,840],{"className":3214,"style":870},[631,635],[570,3216],{"className":3217,"style":674},[673],[570,3219,602],{"className":3220},[678],[570,3222],{"className":3223,"style":674},[673],[570,3225,3227,3230,3233,3236,3239],{"className":3226},[622],[570,3228],{"className":3229,"style":688},[626],[570,3231,1725],{"className":3232},[631],[570,3234],{"className":3235,"style":893},[673],[570,3237,605],{"className":3238},[897],[570,3240],{"className":3241,"style":893},[673],[570,3243,3245,3248,3251],{"className":3244},[622],[570,3246],{"className":3247,"style":730},[626],[570,3249,2025],{"className":3250},[631],[570,3252,718],{"className":3253},[631,635],[570,3255,3257,3281],{"className":3256},[573],[570,3258,3260],{"className":3259},[577],[579,3261,3262],{"xmlns":581},[583,3263,3264,3278],{},[586,3265,3266,3268,3270,3272,3274,3276],{},[592,3267,1047],{"mathvariant":972},[600,3269,976],{},[592,3271,840],{},[600,3273,602],{},[600,3275,605],{},[596,3277,2025],{},[610,3279,3280],{"encoding":612},"\\operatorname{Im} z = -5",[570,3282,3284,3311],{"className":3283,"ariaHidden":618},[617],[570,3285,3287,3290,3296,3299,3302,3305,3308],{"className":3286},[622],[570,3288],{"className":3289,"style":995},[626],[570,3291,3293],{"className":3292},[999],[570,3294,1047],{"className":3295},[631,1003],[570,3297],{"className":3298,"style":1007},[673],[570,3300,840],{"className":3301,"style":870},[631,635],[570,3303],{"className":3304,"style":674},[673],[570,3306,602],{"className":3307},[678],[570,3309],{"className":3310,"style":674},[673],[570,3312,3314,3317,3320],{"className":3313},[622],[570,3315],{"className":3316,"style":688},[626],[570,3318,605],{"className":3319},[631],[570,3321,2025],{"className":3322},[631],", nicht ",[570,3325,3327,3345],{"className":3326},[573],[570,3328,3330],{"className":3329},[577],[579,3331,3332],{"xmlns":581},[583,3333,3334,3342],{},[586,3335,3336,3338,3340],{},[600,3337,605],{},[596,3339,2025],{},[592,3341,718],{},[610,3343,3344],{"encoding":612},"-5i",[570,3346,3348],{"className":3347,"ariaHidden":618},[617],[570,3349,3351,3354,3357,3360],{"className":3350},[622],[570,3352],{"className":3353,"style":2414},[626],[570,3355,605],{"className":3356},[631],[570,3358,2025],{"className":3359},[631],[570,3361,718],{"className":3362},[631,635],[951,3364,3365,3366,3654,3655,946],{},"Das Wurzelgesetz für negative Radikanden verwenden: ",[570,3367,3369,3412],{"className":3368},[573],[570,3370,3372],{"className":3371},[577],[579,3373,3374],{"xmlns":581},[583,3375,3376,3409],{},[586,3377,3378,3386,3388,3397,3399,3404,3406],{},[2747,3379,3380],{},[586,3381,3382,3384],{},[600,3383,605],{},[596,3385,1654],{},[600,3387,2198],{},[2747,3389,3390],{},[586,3391,3392,3394],{},[600,3393,605],{},[596,3395,3396],{},"9",[600,3398,1252],{"mathvariant":972},[2747,3400,3401],{},[596,3402,3403],{},"36",[600,3405,602],{},[596,3407,3408],{},"6",[610,3410,3411],{"encoding":612},"\\sqrt{-4} \\cdot \\sqrt{-9} \\neq \\sqrt{36} = 6",[570,3413,3415,3480,3579,3645],{"className":3414,"ariaHidden":618},[617],[570,3416,3418,3421,3471,3474,3477],{"className":3417},[622],[570,3419],{"className":3420,"style":2773},[626],[570,3422,3424],{"className":3423},[631,2777],[570,3425,3427,3463],{"className":3426},[643,2781],[570,3428,3430,3460],{"className":3429},[647],[570,3431,3433,3448],{"className":3432,"style":2788},[651],[570,3434,3436,3439],{"className":3435,"style":2793},[2792],[570,3437],{"className":3438,"style":2797},[658],[570,3440,3442,3445],{"className":3441,"style":2801},[631],[570,3443,605],{"className":3444},[631],[570,3446,1654],{"className":3447},[631],[570,3449,3450,3453],{"style":2810},[570,3451],{"className":3452,"style":2797},[658],[570,3454,3456],{"className":3455,"style":2818},[2817],[2820,3457,3458],{"xmlns":2822,"width":2823,"height":2824,"viewBox":2825,"preserveAspectRatio":2826},[2828,3459],{"d":2830},[570,3461,2835],{"className":3462},[2834],[570,3464,3466],{"className":3465},[647],[570,3467,3469],{"className":3468,"style":2842},[651],[570,3470],{},[570,3472],{"className":3473,"style":893},[673],[570,3475,2198],{"className":3476},[897],[570,3478],{"className":3479,"style":893},[673],[570,3481,3483,3487,3537,3540,3576],{"className":3482},[622],[570,3484],{"className":3485,"style":3486},[626],"height:1.06em;vertical-align:-0.1944em;",[570,3488,3490],{"className":3489},[631,2777],[570,3491,3493,3529],{"className":3492},[643,2781],[570,3494,3496,3526],{"className":3495},[647],[570,3497,3499,3514],{"className":3498,"style":2788},[651],[570,3500,3502,3505],{"className":3501,"style":2793},[2792],[570,3503],{"className":3504,"style":2797},[658],[570,3506,3508,3511],{"className":3507,"style":2801},[631],[570,3509,605],{"className":3510},[631],[570,3512,3396],{"className":3513},[631],[570,3515,3516,3519],{"style":2810},[570,3517],{"className":3518,"style":2797},[658],[570,3520,3522],{"className":3521,"style":2818},[2817],[2820,3523,3524],{"xmlns":2822,"width":2823,"height":2824,"viewBox":2825,"preserveAspectRatio":2826},[2828,3525],{"d":2830},[570,3527,2835],{"className":3528},[2834],[570,3530,3532],{"className":3531},[647],[570,3533,3535],{"className":3534,"style":2842},[651],[570,3536],{},[570,3538],{"className":3539,"style":674},[673],[570,3541,3543,3570,3573],{"className":3542},[678],[570,3544,3546],{"className":3545},[678],[570,3547,3549],{"className":3548},[631,1283],[570,3550,3552],{"className":3551},[1287],[570,3553,3555,3558,3567],{"className":3554},[1291],[570,3556],{"className":3557,"style":1267},[626],[570,3559,3561],{"className":3560},[1298],[570,3562,3564],{"className":3563},[631],[570,3565,1305],{"className":3566},[678],[570,3568],{"className":3569},[1309],[570,3571],{"className":3572},[673,1313],[570,3574,602],{"className":3575},[678],[570,3577],{"className":3578,"style":674},[673],[570,3580,3582,3586,3636,3639,3642],{"className":3581},[622],[570,3583],{"className":3584,"style":3585},[626],"height:1.04em;vertical-align:-0.1328em;",[570,3587,3589],{"className":3588},[631,2777],[570,3590,3592,3627],{"className":3591},[643,2781],[570,3593,3595,3624],{"className":3594},[647],[570,3596,3599,3611],{"className":3597,"style":3598},[651],"height:0.9072em;",[570,3600,3602,3605],{"className":3601,"style":2793},[2792],[570,3603],{"className":3604,"style":2797},[658],[570,3606,3608],{"className":3607,"style":2801},[631],[570,3609,3403],{"className":3610},[631],[570,3612,3614,3617],{"style":3613},"top:-2.8672em;",[570,3615],{"className":3616,"style":2797},[658],[570,3618,3620],{"className":3619,"style":2818},[2817],[2820,3621,3622],{"xmlns":2822,"width":2823,"height":2824,"viewBox":2825,"preserveAspectRatio":2826},[2828,3623],{"d":2830},[570,3625,2835],{"className":3626},[2834],[570,3628,3630],{"className":3629},[647],[570,3631,3634],{"className":3632,"style":3633},[651],"height:0.1328em;",[570,3635],{},[570,3637],{"className":3638,"style":674},[673],[570,3640,602],{"className":3641},[678],[570,3643],{"className":3644,"style":674},[673],[570,3646,3648,3651],{"className":3647},[622],[570,3649],{"className":3650,"style":1151},[626],[570,3652,3408],{"className":3653},[631],". Richtig ist ",[570,3656,3658,3696],{"className":3657},[573],[570,3659,3661],{"className":3660},[577],[579,3662,3663],{"xmlns":581},[583,3664,3665,3693],{},[586,3666,3667,3669,3671,3673,3675,3677,3679,3681,3687,3689,3691],{},[596,3668,598],{},[592,3670,718],{},[600,3672,2198],{},[596,3674,1725],{},[592,3676,718],{},[600,3678,602],{},[596,3680,3408],{},[589,3682,3683,3685],{},[592,3684,718],{},[596,3686,598],{},[600,3688,602],{},[600,3690,605],{},[596,3692,3408],{},[610,3694,3695],{"encoding":612},"2i \\cdot 3i = 6i^2 = -6",[570,3697,3699,3720,3741,3788],{"className":3698,"ariaHidden":618},[617],[570,3700,3702,3705,3708,3711,3714,3717],{"className":3701},[622],[570,3703],{"className":3704,"style":730},[626],[570,3706,598],{"className":3707},[631],[570,3709,718],{"className":3710},[631,635],[570,3712],{"className":3713,"style":893},[673],[570,3715,2198],{"className":3716},[897],[570,3718],{"className":3719,"style":893},[673],[570,3721,3723,3726,3729,3732,3735,3738],{"className":3722},[622],[570,3724],{"className":3725,"style":730},[626],[570,3727,1725],{"className":3728},[631],[570,3730,718],{"className":3731},[631,635],[570,3733],{"className":3734,"style":674},[673],[570,3736,602],{"className":3737},[678],[570,3739],{"className":3740,"style":674},[673],[570,3742,3744,3747,3750,3779,3782,3785],{"className":3743},[622],[570,3745],{"className":3746,"style":627},[626],[570,3748,3408],{"className":3749},[631],[570,3751,3753,3756],{"className":3752},[631],[570,3754,718],{"className":3755},[631,635],[570,3757,3759],{"className":3758},[639],[570,3760,3762],{"className":3761},[643],[570,3763,3765],{"className":3764},[647],[570,3766,3768],{"className":3767,"style":627},[651],[570,3769,3770,3773],{"style":654},[570,3771],{"className":3772,"style":659},[658],[570,3774,3776],{"className":3775},[663,664,665,666],[570,3777,598],{"className":3778},[631,666],[570,3780],{"className":3781,"style":674},[673],[570,3783,602],{"className":3784},[678],[570,3786],{"className":3787,"style":674},[673],[570,3789,3791,3794,3797],{"className":3790},[622],[570,3792],{"className":3793,"style":688},[626],[570,3795,605],{"className":3796},[631],[570,3798,3408],{"className":3799},[631],[951,3801,3802,3883,3884,3969],{},[570,3803,3805,3827],{"className":3804},[573],[570,3806,3808],{"className":3807},[577],[579,3809,3810],{"xmlns":581},[583,3811,3812,3824],{},[586,3813,3814,3820,3822],{},[589,3815,3816,3818],{},[592,3817,718],{},[596,3819,598],{},[600,3821,602],{},[596,3823,608],{},[610,3825,3826],{"encoding":612},"i^2 = 1",[570,3828,3830,3874],{"className":3829,"ariaHidden":618},[617],[570,3831,3833,3836,3865,3868,3871],{"className":3832},[622],[570,3834],{"className":3835,"style":627},[626],[570,3837,3839,3842],{"className":3838},[631],[570,3840,718],{"className":3841},[631,635],[570,3843,3845],{"className":3844},[639],[570,3846,3848],{"className":3847},[643],[570,3849,3851],{"className":3850},[647],[570,3852,3854],{"className":3853,"style":627},[651],[570,3855,3856,3859],{"style":654},[570,3857],{"className":3858,"style":659},[658],[570,3860,3862],{"className":3861},[663,664,665,666],[570,3863,598],{"className":3864},[631,666],[570,3866],{"className":3867,"style":674},[673],[570,3869,602],{"className":3870},[678],[570,3872],{"className":3873,"style":674},[673],[570,3875,3877,3880],{"className":3876},[622],[570,3878],{"className":3879,"style":1151},[626],[570,3881,608],{"className":3882},[631]," rechnen. Die imaginäre Einheit ist gerade so festgelegt, dass ",[570,3885,3887,3910],{"className":3886},[573],[570,3888,3890],{"className":3889},[577],[579,3891,3892],{"xmlns":581},[583,3893,3894,3908],{},[586,3895,3896,3902,3904,3906],{},[589,3897,3898,3900],{},[592,3899,718],{},[596,3901,598],{},[600,3903,602],{},[600,3905,605],{},[596,3907,608],{},[610,3909,761],{"encoding":612},[570,3911,3913,3957],{"className":3912,"ariaHidden":618},[617],[570,3914,3916,3919,3948,3951,3954],{"className":3915},[622],[570,3917],{"className":3918,"style":627},[626],[570,3920,3922,3925],{"className":3921},[631],[570,3923,718],{"className":3924},[631,635],[570,3926,3928],{"className":3927},[639],[570,3929,3931],{"className":3930},[643],[570,3932,3934],{"className":3933},[647],[570,3935,3937],{"className":3936,"style":627},[651],[570,3938,3939,3942],{"style":654},[570,3940],{"className":3941,"style":659},[658],[570,3943,3945],{"className":3944},[663,664,665,666],[570,3946,598],{"className":3947},[631,666],[570,3949],{"className":3950,"style":674},[673],[570,3952,602],{"className":3953},[678],[570,3955],{"className":3956,"style":674},[673],[570,3958,3960,3963,3966],{"className":3959},[622],[570,3961],{"className":3962,"style":688},[626],[570,3964,605],{"className":3965},[631],[570,3967,608],{"className":3968},[631]," gilt.",[951,3971,3972,3973,4001,4002,4060],{},"Komplexe Zahlen der Größe nach vergleichen. Auf ",[570,3974,3976,3989],{"className":3975},[573],[570,3977,3979],{"className":3978},[577],[579,3980,3981],{"xmlns":581},[583,3982,3983,3987],{},[586,3984,3985],{},[592,3986,928],{"mathvariant":927},[610,3988,931],{"encoding":612},[570,3990,3992],{"className":3991,"ariaHidden":618},[617],[570,3993,3995,3998],{"className":3994},[622],[570,3996],{"className":3997,"style":941},[626],[570,3999,928],{"className":4000},[631,945]," gibt es keine mit den Rechenregeln verträgliche Anordnung; ",[570,4003,4005,4026],{"className":4004},[573],[570,4006,4008],{"className":4007},[577],[579,4009,4010],{"xmlns":581},[583,4011,4012,4023],{},[586,4013,4014,4016,4018,4021],{},[596,4015,598],{},[592,4017,718],{},[600,4019,4020],{},">",[592,4022,718],{},[610,4024,4025],{"encoding":612},"2i > i",[570,4027,4029,4051],{"className":4028,"ariaHidden":618},[617],[570,4030,4032,4036,4039,4042,4045,4048],{"className":4031},[622],[570,4033],{"className":4034,"style":4035},[626],"height:0.6986em;vertical-align:-0.0391em;",[570,4037,598],{"className":4038},[631],[570,4040,718],{"className":4041},[631,635],[570,4043],{"className":4044,"style":674},[673],[570,4046,4020],{"className":4047},[678],[570,4049],{"className":4050,"style":674},[673],[570,4052,4054,4057],{"className":4053},[622],[570,4055],{"className":4056,"style":730},[626],[570,4058,718],{"className":4059},[631,635]," ist keine sinnvolle Aussage.",{"title":4062,"searchDepth":4063,"depth":4063,"links":4064},"",2,[4065,4066,4067],{"id":563,"depth":4063,"text":564},{"id":1986,"depth":4063,"text":1987},{"id":3140,"depth":4063,"text":3141},[4069,4071,4073,4075,4078,4080,4082,4084,4086,4088,4091,4093,4095,4097,4099],{"lhs":4070,"rhs":1594},"re(i^2)",{"lhs":4072,"rhs":1120},"im(i^2)",{"lhs":4074,"rhs":1654},"re((3 + 2*i) + (1 - 5*i))",{"lhs":4076,"rhs":4077},"im((3 + 2*i) + (1 - 5*i))","-3",{"lhs":4079,"rhs":1120},"re(i^3)",{"lhs":4081,"rhs":1594},"im(i^3)",{"lhs":4083,"rhs":608},"re(i^4)",{"lhs":4085,"rhs":1120},"re(i^7)",{"lhs":4087,"rhs":1594},"im(i^7)",{"lhs":4089,"rhs":4090},"2^2 - 4*1*5","-16",{"lhs":4092,"rhs":1120},"re((-1 + 2*i)^2 + 2*(-1 + 2*i) + 5)",{"lhs":4094,"rhs":1120},"im((-1 + 2*i)^2 + 2*(-1 + 2*i) + 5)",{"lhs":4096,"rhs":1120},"re((-1 - 2*i)^2 + 2*(-1 - 2*i) + 5)",{"lhs":4098,"rhs":1120},"im((-1 - 2*i)^2 + 2*(-1 - 2*i) + 5)",{"lhs":4100,"rhs":4101},"re((2*i) * (3*i))","-6","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>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-number-form","z = a + bi, \\qquad i^2 = -1","\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>\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>\u003Cmspace width=\"2em\"\u002F>\u003Cmsup>\u003Cmi>i\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">z = a + bi, \\qquad i^2 = -1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\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:1.0585em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">bi\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">i\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Falgebra\u002Fkomplexe-zahl",[],[4115,4116,4117,4118],"complex-modulus","complex-conjugate","complex-multiplication","polar-form",{"title":548,"description":4062},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fkomplexe-zahl","Eine komplexe Zahl besteht aus Realteil a und Imaginärteil b, die imaginäre Einheit i erfüllt i² = −1.",[4123,4124,4125,4126,4127],"komplexe zahlen","imaginäre einheit","realteil","imaginärteil","gaußsche zahlenebene",[4129,4132,4135,4138],{"symbol":840,"meaning":4130,"symbolHtml":4131},"komplexe Zahl","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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":845,"meaning":4133,"symbolHtml":4134},"Realteil, a = Re 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":851,"meaning":4136,"symbolHtml":4137},"Imaginärteil, b = Im z (eine reelle Zahl, ohne i)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":718,"meaning":552,"symbolHtml":4139},"\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">i\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:0.6595em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","3fWHPJ455aa3qGT59yigAzUQiOvCtZrgMaLvq4TZX88",[4142,4145,4148,4151],{"stem":4143,"title":4144,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fbetrag-komplexe-zahl","Betrag einer komplexen Zahl",{"stem":4146,"title":4147,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fkonjugiert-komplexe-zahl","Konjugiert komplexe Zahl",{"stem":4149,"title":4150,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fmultiplikation-komplexer-zahlen","Multiplikation komplexer Zahlen",{"stem":4152,"title":4153,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fpolarform-komplexe-zahl","Polarform einer komplexen Zahl",1793824272173]