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Für den Kehrwert gilt",[568,1159,1162],{"className":1160},[1161],"katex-display",[568,1163,1165,1212],{"className":1164},[571],[568,1166,1168],{"className":1167},[575],[577,1169,1171],{"xmlns":579,"display":1170},"block",[581,1172,1173,1209],{},[584,1174,1175,1184,1186],{},[1176,1177,1178,1181],"mfrac",{},[707,1179,1180],{},"1",[587,1182,1183],{},"z",[591,1185,700],{},[1176,1187,1188,1196],{},[1189,1190,1191,1193],"mover",{"accent":609},[587,1192,1183],{},[591,1194,1195],{"stretchy":609},"‾",[584,1197,1198,1201,1203],{},[587,1199,1200],{"mathvariant":987},"∣",[587,1202,1183],{},[702,1204,1205,1207],{},[587,1206,1200],{"mathvariant":987},[707,1208,709],{},[601,1210,1211],{"encoding":603},"\\frac{1}{z} = \\frac{\\overline{z}}{|z|^2}",[568,1213,1215,1306],{"className":1214,"ariaHidden":609},[608],[568,1216,1218,1222,1297,1300,1303],{"className":1217},[613],[568,1219],{"className":1220,"style":1221},[617],"height:2.0074em;vertical-align:-0.686em;",[568,1223,1225,1229,1294],{"className":1224},[622],[568,1226],{"className":1227},[734,1228],"nulldelimiter",[568,1230,1232],{"className":1231},[1176],[568,1233,1236,1285],{"className":1234},[824,1235],"vlist-t2",[568,1237,1239,1280],{"className":1238},[828],[568,1240,1243,1257,1268],{"className":1241,"style":1242},[832],"height:1.3214em;",[568,1244,1246,1250],{"style":1245},"top:-2.314em;",[568,1247],{"className":1248,"style":1249},[840],"height:3em;",[568,1251,1253],{"className":1252},[622],[568,1254,1183],{"className":1255,"style":1256},[622,623],"margin-right:0.044em;",[568,1258,1260,1263],{"style":1259},"top:-3.23em;",[568,1261],{"className":1262,"style":1249},[840],[568,1264],{"className":1265,"style":1267},[1266],"frac-line","border-bottom-width:0.04em;",[568,1269,1271,1274],{"style":1270},"top:-3.677em;",[568,1272],{"className":1273,"style":1249},[840],[568,1275,1277],{"className":1276},[622],[568,1278,1180],{"className":1279},[622],[568,1281,1284],{"className":1282},[1283],"vlist-s","​",[568,1286,1288],{"className":1287},[828],[568,1289,1292],{"className":1290,"style":1291},[832],"height:0.686em;",[568,1293],{},[568,1295],{"className":1296},[762,1228],[568,1298],{"className":1299,"style":796},[627],[568,1301,700],{"className":1302},[800],[568,1304],{"className":1305,"style":796},[627],[568,1307,1309,1313],{"className":1308},[613],[568,1310],{"className":1311,"style":1312},[617],"height:2.2436em;vertical-align:-0.936em;",[568,1314,1316,1319,1441],{"className":1315},[622],[568,1317],{"className":1318},[734,1228],[568,1320,1322],{"className":1321},[1176],[568,1323,1325,1432],{"className":1324},[824,1235],[568,1326,1328,1429],{"className":1327},[828],[568,1329,1332,1377,1385],{"className":1330,"style":1331},[832],"height:1.3076em;",[568,1333,1334,1337],{"style":1245},[568,1335],{"className":1336,"style":1249},[840],[568,1338,1340,1343,1346],{"className":1339},[622],[568,1341,1200],{"className":1342},[622],[568,1344,1183],{"className":1345,"style":1256},[622,623],[568,1347,1349,1352],{"className":1348},[622],[568,1350,1200],{"className":1351},[622],[568,1353,1355],{"className":1354},[820],[568,1356,1358],{"className":1357},[824],[568,1359,1361],{"className":1360},[828],[568,1362,1365],{"className":1363,"style":1364},[832],"height:0.7401em;",[568,1366,1368,1371],{"style":1367},"top:-2.989em;margin-right:0.05em;",[568,1369],{"className":1370,"style":841},[840],[568,1372,1374],{"className":1373},[845,846,847,848],[568,1375,709],{"className":1376},[622,848],[568,1378,1379,1382],{"style":1259},[568,1380],{"className":1381,"style":1249},[840],[568,1383],{"className":1384,"style":1267},[1266],[568,1386,1387,1390],{"style":1270},[568,1388],{"className":1389,"style":1249},[840],[568,1391,1393],{"className":1392},[622],[568,1394,1397],{"className":1395},[622,1396],"overline",[568,1398,1400],{"className":1399},[824],[568,1401,1403],{"className":1402},[828],[568,1404,1407,1419],{"className":1405,"style":1406},[832],"height:0.6306em;",[568,1408,1410,1413],{"style":1409},"top:-3em;",[568,1411],{"className":1412,"style":1249},[840],[568,1414,1416],{"className":1415},[622],[568,1417,1183],{"className":1418,"style":1256},[622,623],[568,1420,1422,1425],{"style":1421},"top:-3.5506em;",[568,1423],{"className":1424,"style":1249},[840],[568,1426],{"className":1427,"style":1267},[1428],"overline-line",[568,1430,1284],{"className":1431},[1283],[568,1433,1435],{"className":1434},[828],[568,1436,1439],{"className":1437,"style":1438},[832],"height:0.936em;",[568,1440],{},[568,1442],{"className":1443},[762,1228],[559,1445,1447],{"id":1446},"beispiele","Beispiele",[568,1449,1451],{"className":1450},[1161],[568,1452,1454,1611],{"className":1453},[571],[568,1455,1457],{"className":1456},[575],[577,1458,1459],{"xmlns":579,"display":1170},[581,1460,1461,1608],{},[584,1462,1463,1486,1488,1542,1544,1582,1584,1599,1601,1604,1606],{},[1176,1464,1465,1476],{},[584,1466,1467,1470,1472,1474],{},[707,1468,1469],{},"5",[591,1471,593],{},[707,1473,1469],{},[587,1475,599],{},[584,1477,1478,1480,1482,1484],{},[707,1479,1180],{},[591,1481,593],{},[707,1483,709],{},[587,1485,599],{},[591,1487,700],{},[1176,1489,1490,1516],{},[584,1491,1492,1494,1496,1498,1500,1502,1504,1506,1508,1510,1512,1514],{},[591,1493,671],{"stretchy":670},[707,1495,1469],{},[591,1497,593],{},[707,1499,1469],{},[587,1501,599],{},[591,1503,684],{"stretchy":670},[591,1505,671],{"stretchy":670},[707,1507,1180],{},[591,1509,691],{},[707,1511,709],{},[587,1513,599],{},[591,1515,684],{"stretchy":670},[584,1517,1518,1520,1522,1524,1526,1528,1530,1532,1534,1536,1538,1540],{},[591,1519,671],{"stretchy":670},[707,1521,1180],{},[591,1523,593],{},[707,1525,709],{},[587,1527,599],{},[591,1529,684],{"stretchy":670},[591,1531,671],{"stretchy":670},[707,1533,1180],{},[591,1535,691],{},[707,1537,709],{},[587,1539,599],{},[591,1541,684],{"stretchy":670},[591,1543,700],{},[1176,1545,1546,1573],{},[584,1547,1548,1550,1552,1555,1557,1559,1561,1563,1565,1567],{},[707,1549,1469],{},[591,1551,691],{},[707,1553,1554],{},"10",[587,1556,599],{},[591,1558,593],{},[707,1560,1469],{},[587,1562,599],{},[591,1564,691],{},[707,1566,1554],{},[702,1568,1569,1571],{},[587,1570,599],{},[707,1572,709],{},[584,1574,1575,1577,1579],{},[707,1576,1180],{},[591,1578,593],{},[707,1580,1581],{},"4",[591,1583,700],{},[1176,1585,1586,1597],{},[584,1587,1588,1591,1593,1595],{},[707,1589,1590],{},"15",[591,1592,691],{},[707,1594,1469],{},[587,1596,599],{},[707,1598,1469],{},[591,1600,700],{},[707,1602,1603],{},"3",[591,1605,691],{},[587,1607,599],{},[601,1609,1610],{"encoding":603},"\\frac{5 + 5i}{1 + 2i}\n= \\frac{(5 + 5i)(1 - 2i)}{(1 + 2i)(1 - 2i)}\n= \\frac{5 - 10i + 5i - 10i^2}{1 + 4}\n= \\frac{15 - 5i}{5}\n= 3 - i",[568,1612,1614,1724,1893,2055,2148,2167],{"className":1613,"ariaHidden":609},[608],[568,1615,1617,1621,1715,1718,1721],{"className":1616},[613],[568,1618],{"className":1619,"style":1620},[617],"height:2.1059em;vertical-align:-0.7693em;",[568,1622,1624,1627,1712],{"className":1623},[622],[568,1625],{"className":1626},[734,1228],[568,1628,1630],{"className":1629},[1176],[568,1631,1633,1703],{"className":1632},[824,1235],[568,1634,1636,1700],{"className":1635},[828],[568,1637,1640,1666,1674],{"className":1638,"style":1639},[832],"height:1.3365em;",[568,1641,1642,1645],{"style":1245},[568,1643],{"className":1644,"style":1249},[840],[568,1646,1648,1651,1654,1657,1660,1663],{"className":1647},[622],[568,1649,1180],{"className":1650},[622],[568,1652],{"className":1653,"style":628},[627],[568,1655,593],{"className":1656},[632],[568,1658],{"className":1659,"style":628},[627],[568,1661,709],{"className":1662},[622],[568,1664,599],{"className":1665},[622,623],[568,1667,1668,1671],{"style":1259},[568,1669],{"className":1670,"style":1249},[840],[568,1672],{"className":1673,"style":1267},[1266],[568,1675,1676,1679],{"style":1270},[568,1677],{"className":1678,"style":1249},[840],[568,1680,1682,1685,1688,1691,1694,1697],{"className":1681},[622],[568,1683,1469],{"className":1684},[622],[568,1686],{"className":1687,"style":628},[627],[568,1689,593],{"className":1690},[632],[568,1692],{"className":1693,"style":628},[627],[568,1695,1469],{"className":1696},[622],[568,1698,599],{"className":1699},[622,623],[568,1701,1284],{"className":1702},[1283],[568,1704,1706],{"className":1705},[828],[568,1707,1710],{"className":1708,"style":1709},[832],"height:0.7693em;",[568,1711],{},[568,1713],{"className":1714},[762,1228],[568,1716],{"className":1717,"style":796},[627],[568,1719,700],{"className":1720},[800],[568,1722],{"className":1723,"style":796},[627],[568,1725,1727,1731,1884,1887,1890],{"className":1726},[613],[568,1728],{"className":1729,"style":1730},[617],"height:2.363em;vertical-align:-0.936em;",[568,1732,1734,1737,1881],{"className":1733},[622],[568,1735],{"className":1736},[734,1228],[568,1738,1740],{"className":1739},[1176],[568,1741,1743,1873],{"className":1742},[824,1235],[568,1744,1746,1870],{"className":1745},[828],[568,1747,1750,1806,1814],{"className":1748,"style":1749},[832],"height:1.427em;",[568,1751,1752,1755],{"style":1245},[568,1753],{"className":1754,"style":1249},[840],[568,1756,1758,1761,1764,1767,1770,1773,1776,1779,1782,1785,1788,1791,1794,1797,1800,1803],{"className":1757},[622],[568,1759,671],{"className":1760},[734],[568,1762,1180],{"className":1763},[622],[568,1765],{"className":1766,"style":628},[627],[568,1768,593],{"className":1769},[632],[568,1771],{"className":1772,"style":628},[627],[568,1774,709],{"className":1775},[622],[568,1777,599],{"className":1778},[622,623],[568,1780,684],{"className":1781},[762],[568,1783,671],{"className":1784},[734],[568,1786,1180],{"className":1787},[622],[568,1789],{"className":1790,"style":628},[627],[568,1792,691],{"className":1793},[632],[568,1795],{"className":1796,"style":628},[627],[568,1798,709],{"className":1799},[622],[568,1801,599],{"className":1802},[622,623],[568,1804,684],{"className":1805},[762],[568,1807,1808,1811],{"style":1259},[568,1809],{"className":1810,"style":1249},[840],[568,1812],{"className":1813,"style":1267},[1266],[568,1815,1816,1819],{"style":1270},[568,1817],{"className":1818,"style":1249},[840],[568,1820,1822,1825,1828,1831,1834,1837,1840,1843,1846,1849,1852,1855,1858,1861,1864,1867],{"className":1821},[622],[568,1823,671],{"className":1824},[734],[568,1826,1469],{"className":1827},[622],[568,1829],{"className":1830,"style":628},[627],[568,1832,593],{"className":1833},[632],[568,1835],{"className":1836,"style":628},[627],[568,1838,1469],{"className":1839},[622],[568,1841,599],{"className":1842},[622,623],[568,1844,684],{"className":1845},[762],[568,1847,671],{"className":1848},[734],[568,1850,1180],{"className":1851},[622],[568,1853],{"className":1854,"style":628},[627],[568,1856,691],{"className":1857},[632],[568,1859],{"className":1860,"style":628},[627],[568,1862,709],{"className":1863},[622],[568,1865,599],{"className":1866},[622,623],[568,1868,684],{"className":1869},[762],[568,1871,1284],{"className":1872},[1283],[568,1874,1876],{"className":1875},[828],[568,1877,1879],{"className":1878,"style":1438},[832],[568,1880],{},[568,1882],{"className":1883},[762,1228],[568,1885],{"className":1886,"style":796},[627],[568,1888,700],{"className":1889},[800],[568,1891],{"className":1892,"style":796},[627],[568,1894,1896,1900,2046,2049,2052],{"className":1895},[613],[568,1897],{"className":1898,"style":1899},[617],"height:2.2604em;vertical-align:-0.7693em;",[568,1901,1903,1906,2043],{"className":1902},[622],[568,1904],{"className":1905},[734,1228],[568,1907,1909],{"className":1908},[1176],[568,1910,1912,2035],{"className":1911},[824,1235],[568,1913,1915,2032],{"className":1914},[828],[568,1916,1919,1942,1950],{"className":1917,"style":1918},[832],"height:1.4911em;",[568,1920,1921,1924],{"style":1245},[568,1922],{"className":1923,"style":1249},[840],[568,1925,1927,1930,1933,1936,1939],{"className":1926},[622],[568,1928,1180],{"className":1929},[622],[568,1931],{"className":1932,"style":628},[627],[568,1934,593],{"className":1935},[632],[568,1937],{"className":1938,"style":628},[627],[568,1940,1581],{"className":1941},[622],[568,1943,1944,1947],{"style":1259},[568,1945],{"className":1946,"style":1249},[840],[568,1948],{"className":1949,"style":1267},[1266],[568,1951,1952,1955],{"style":1270},[568,1953],{"className":1954,"style":1249},[840],[568,1956,1958,1961,1964,1967,1970,1973,1976,1979,1982,1985,1988,1991,1994,1997,2000,2003],{"className":1957},[622],[568,1959,1469],{"className":1960},[622],[568,1962],{"className":1963,"style":628},[627],[568,1965,691],{"className":1966},[632],[568,1968],{"className":1969,"style":628},[627],[568,1971,1554],{"className":1972},[622],[568,1974,599],{"className":1975},[622,623],[568,1977],{"className":1978,"style":628},[627],[568,1980,593],{"className":1981},[632],[568,1983],{"className":1984,"style":628},[627],[568,1986,1469],{"className":1987},[622],[568,1989,599],{"className":1990},[622,623],[568,1992],{"className":1993,"style":628},[627],[568,1995,691],{"className":1996},[632],[568,1998],{"className":1999,"style":628},[627],[568,2001,1554],{"className":2002},[622],[568,2004,2006,2009],{"className":2005},[622],[568,2007,599],{"className":2008},[622,623],[568,2010,2012],{"className":2011},[820],[568,2013,2015],{"className":2014},[824],[568,2016,2018],{"className":2017},[828],[568,2019,2021],{"className":2020,"style":833},[832],[568,2022,2023,2026],{"style":836},[568,2024],{"className":2025,"style":841},[840],[568,2027,2029],{"className":2028},[845,846,847,848],[568,2030,709],{"className":2031},[622,848],[568,2033,1284],{"className":2034},[1283],[568,2036,2038],{"className":2037},[828],[568,2039,2041],{"className":2040,"style":1709},[832],[568,2042],{},[568,2044],{"className":2045},[762,1228],[568,2047],{"className":2048,"style":796},[627],[568,2050,700],{"className":2051},[800],[568,2053],{"className":2054,"style":796},[627],[568,2056,2058,2062,2139,2142,2145],{"className":2057},[613],[568,2059],{"className":2060,"style":2061},[617],"height:2.0225em;vertical-align:-0.686em;",[568,2063,2065,2068,2136],{"className":2064},[622],[568,2066],{"className":2067},[734,1228],[568,2069,2071],{"className":2070},[1176],[568,2072,2074,2128],{"className":2073},[824,1235],[568,2075,2077,2125],{"className":2076},[828],[568,2078,2080,2091,2099],{"className":2079,"style":1639},[832],[568,2081,2082,2085],{"style":1245},[568,2083],{"className":2084,"style":1249},[840],[568,2086,2088],{"className":2087},[622],[568,2089,1469],{"className":2090},[622],[568,2092,2093,2096],{"style":1259},[568,2094],{"className":2095,"style":1249},[840],[568,2097],{"className":2098,"style":1267},[1266],[568,2100,2101,2104],{"style":1270},[568,2102],{"className":2103,"style":1249},[840],[568,2105,2107,2110,2113,2116,2119,2122],{"className":2106},[622],[568,2108,1590],{"className":2109},[622],[568,2111],{"className":2112,"style":628},[627],[568,2114,691],{"className":2115},[632],[568,2117],{"className":2118,"style":628},[627],[568,2120,1469],{"className":2121},[622],[568,2123,599],{"className":2124},[622,623],[568,2126,1284],{"className":2127},[1283],[568,2129,2131],{"className":2130},[828],[568,2132,2134],{"className":2133,"style":1291},[832],[568,2135],{},[568,2137],{"className":2138},[762,1228],[568,2140],{"className":2141,"style":796},[627],[568,2143,700],{"className":2144},[800],[568,2146],{"className":2147,"style":796},[627],[568,2149,2151,2155,2158,2161,2164],{"className":2150},[613],[568,2152],{"className":2153,"style":2154},[617],"height:0.7278em;vertical-align:-0.0833em;",[568,2156,1603],{"className":2157},[622],[568,2159],{"className":2160,"style":628},[627],[568,2162,691],{"className":2163},[632],[568,2165],{"className":2166,"style":628},[627],[568,2168,2170,2174],{"className":2169},[613],[568,2171],{"className":2172,"style":2173},[617],"height:0.6595em;",[568,2175,599],{"className":2176},[622,623],[568,2178,2180],{"className":2179},[1161],[568,2181,2183,2252],{"className":2182},[571],[568,2184,2186],{"className":2185},[575],[577,2187,2188],{"xmlns":579,"display":1170},[581,2189,2190,2249],{},[584,2191,2192,2198,2200,2231,2233,2243,2245,2247],{},[1176,2193,2194,2196],{},[707,2195,1180],{},[587,2197,599],{},[591,2199,700],{},[1176,2201,2202,2217],{},[584,2203,2204,2206,2209,2211,2213,2215],{},[707,2205,1180],{},[591,2207,2208],{},"⋅",[591,2210,671],{"stretchy":670},[591,2212,691],{},[587,2214,599],{},[591,2216,684],{"stretchy":670},[584,2218,2219,2221,2223,2225,2227,2229],{},[587,2220,599],{},[591,2222,2208],{},[591,2224,671],{"stretchy":670},[591,2226,691],{},[587,2228,599],{},[591,2230,684],{"stretchy":670},[591,2232,700],{},[1176,2234,2235,2241],{},[584,2236,2237,2239],{},[591,2238,691],{},[587,2240,599],{},[707,2242,1180],{},[591,2244,700],{},[591,2246,691],{},[587,2248,599],{},[601,2250,2251],{"encoding":603},"\\frac{1}{i} = \\frac{1 \\cdot (-i)}{i \\cdot (-i)} = \\frac{-i}{1} = -i",[568,2253,2255,2332,2451,2531],{"className":2254,"ariaHidden":609},[608],[568,2256,2258,2261,2323,2326,2329],{"className":2257},[613],[568,2259],{"className":2260,"style":1221},[617],[568,2262,2264,2267,2320],{"className":2263},[622],[568,2265],{"className":2266},[734,1228],[568,2268,2270],{"className":2269},[1176],[568,2271,2273,2312],{"className":2272},[824,1235],[568,2274,2276,2309],{"className":2275},[828],[568,2277,2279,2290,2298],{"className":2278,"style":1242},[832],[568,2280,2281,2284],{"style":1245},[568,2282],{"className":2283,"style":1249},[840],[568,2285,2287],{"className":2286},[622],[568,2288,599],{"className":2289},[622,623],[568,2291,2292,2295],{"style":1259},[568,2293],{"className":2294,"style":1249},[840],[568,2296],{"className":2297,"style":1267},[1266],[568,2299,2300,2303],{"style":1270},[568,2301],{"className":2302,"style":1249},[840],[568,2304,2306],{"className":2305},[622],[568,2307,1180],{"className":2308},[622],[568,2310,1284],{"className":2311},[1283],[568,2313,2315],{"className":2314},[828],[568,2316,2318],{"className":2317,"style":1291},[832],[568,2319],{},[568,2321],{"className":2322},[762,1228],[568,2324],{"className":2325,"style":796},[627],[568,2327,700],{"className":2328},[800],[568,2330],{"className":2331,"style":796},[627],[568,2333,2335,2338,2442,2445,2448],{"className":2334},[613],[568,2336],{"className":2337,"style":1730},[617],[568,2339,2341,2344,2439],{"className":2340},[622],[568,2342],{"className":2343},[734,1228],[568,2345,2347],{"className":2346},[1176],[568,2348,2350,2431],{"className":2349},[824,1235],[568,2351,2353,2428],{"className":2352},[828],[568,2354,2356,2388,2396],{"className":2355,"style":1749},[832],[568,2357,2358,2361],{"style":1245},[568,2359],{"className":2360,"style":1249},[840],[568,2362,2364,2367,2370,2373,2376,2379,2382,2385],{"className":2363},[622],[568,2365,599],{"className":2366},[622,623],[568,2368],{"className":2369,"style":628},[627],[568,2371,2208],{"className":2372},[632],[568,2374],{"className":2375,"style":628},[627],[568,2377,671],{"className":2378},[734],[568,2380,691],{"className":2381},[622],[568,2383,599],{"className":2384},[622,623],[568,2386,684],{"className":2387},[762],[568,2389,2390,2393],{"style":1259},[568,2391],{"className":2392,"style":1249},[840],[568,2394],{"className":2395,"style":1267},[1266],[568,2397,2398,2401],{"style":1270},[568,2399],{"className":2400,"style":1249},[840],[568,2402,2404,2407,2410,2413,2416,2419,2422,2425],{"className":2403},[622],[568,2405,1180],{"className":2406},[622],[568,2408],{"className":2409,"style":628},[627],[568,2411,2208],{"className":2412},[632],[568,2414],{"className":2415,"style":628},[627],[568,2417,671],{"className":2418},[734],[568,2420,691],{"className":2421},[622],[568,2423,599],{"className":2424},[622,623],[568,2426,684],{"className":2427},[762],[568,2429,1284],{"className":2430},[1283],[568,2432,2434],{"className":2433},[828],[568,2435,2437],{"className":2436,"style":1438},[832],[568,2438],{},[568,2440],{"className":2441},[762,1228],[568,2443],{"className":2444,"style":796},[627],[568,2446,700],{"className":2447},[800],[568,2449],{"className":2450,"style":796},[627],[568,2452,2454,2457,2522,2525,2528],{"className":2453},[613],[568,2455],{"className":2456,"style":2061},[617],[568,2458,2460,2463,2519],{"className":2459},[622],[568,2461],{"className":2462},[734,1228],[568,2464,2466],{"className":2465},[1176],[568,2467,2469,2511],{"className":2468},[824,1235],[568,2470,2472,2508],{"className":2471},[828],[568,2473,2475,2486,2494],{"className":2474,"style":1639},[832],[568,2476,2477,2480],{"style":1245},[568,2478],{"className":2479,"style":1249},[840],[568,2481,2483],{"className":2482},[622],[568,2484,1180],{"className":2485},[622],[568,2487,2488,2491],{"style":1259},[568,2489],{"className":2490,"style":1249},[840],[568,2492],{"className":2493,"style":1267},[1266],[568,2495,2496,2499],{"style":1270},[568,2497],{"className":2498,"style":1249},[840],[568,2500,2502,2505],{"className":2501},[622],[568,2503,691],{"className":2504},[622],[568,2506,599],{"className":2507},[622,623],[568,2509,1284],{"className":2510},[1283],[568,2512,2514],{"className":2513},[828],[568,2515,2517],{"className":2516,"style":1291},[832],[568,2518],{},[568,2520],{"className":2521},[762,1228],[568,2523],{"className":2524,"style":796},[627],[568,2526,700],{"className":2527},[800],[568,2529],{"className":2530,"style":796},[627],[568,2532,2534,2538,2541],{"className":2533},[613],[568,2535],{"className":2536,"style":2537},[617],"height:0.7429em;vertical-align:-0.0833em;",[568,2539,691],{"className":2540},[622],[568,2542,599],{"className":2543},[622,623],[564,2545,2546,2547,2603],{},"Kehrwert von ",[568,2548,2550,2570],{"className":2549},[571],[568,2551,2553],{"className":2552},[575],[577,2554,2555],{"xmlns":579},[581,2556,2557,2567],{},[584,2558,2559,2561,2563,2565],{},[707,2560,1603],{},[591,2562,593],{},[707,2564,1581],{},[587,2566,599],{},[601,2568,2569],{"encoding":603},"3 + 4i",[568,2571,2573,2591],{"className":2572,"ariaHidden":609},[608],[568,2574,2576,2579,2582,2585,2588],{"className":2575},[613],[568,2577],{"className":2578,"style":2154},[617],[568,2580,1603],{"className":2581},[622],[568,2583],{"className":2584,"style":628},[627],[568,2586,593],{"className":2587},[632],[568,2589],{"className":2590,"style":628},[627],[568,2592,2594,2597,2600],{"className":2593},[613],[568,2595],{"className":2596,"style":2173},[617],[568,2598,1581],{"className":2599},[622],[568,2601,599],{"className":2602},[622,623],":",[568,2605,2607],{"className":2606},[1161],[568,2608,2610,2665],{"className":2609},[571],[568,2611,2613],{"className":2612},[575],[577,2614,2615],{"xmlns":579,"display":1170},[581,2616,2617,2662],{},[584,2618,2619,2633,2635,2650,2652,2655,2657,2660],{},[1176,2620,2621,2623],{},[707,2622,1180],{},[584,2624,2625,2627,2629,2631],{},[707,2626,1603],{},[591,2628,593],{},[707,2630,1581],{},[587,2632,599],{},[591,2634,700],{},[1176,2636,2637,2647],{},[584,2638,2639,2641,2643,2645],{},[707,2640,1603],{},[591,2642,691],{},[707,2644,1581],{},[587,2646,599],{},[707,2648,2649],{},"25",[591,2651,700],{},[707,2653,2654],{},"0,12",[591,2656,691],{},[707,2658,2659],{},"0,16",[587,2661,599],{},[601,2663,2664],{"encoding":603},"\\frac{1}{3 + 4i} = \\frac{3 - 4i}{25} = 0{,}12 - 0{,}16i",[568,2666,2668,2761,2853,2884],{"className":2667,"ariaHidden":609},[608],[568,2669,2671,2675,2752,2755,2758],{"className":2670},[613],[568,2672],{"className":2673,"style":2674},[617],"height:2.0908em;vertical-align:-0.7693em;",[568,2676,2678,2681,2749],{"className":2677},[622],[568,2679],{"className":2680},[734,1228],[568,2682,2684],{"className":2683},[1176],[568,2685,2687,2741],{"className":2686},[824,1235],[568,2688,2690,2738],{"className":2689},[828],[568,2691,2693,2719,2727],{"className":2692,"style":1242},[832],[568,2694,2695,2698],{"style":1245},[568,2696],{"className":2697,"style":1249},[840],[568,2699,2701,2704,2707,2710,2713,2716],{"className":2700},[622],[568,2702,1603],{"className":2703},[622],[568,2705],{"className":2706,"style":628},[627],[568,2708,593],{"className":2709},[632],[568,2711],{"className":2712,"style":628},[627],[568,2714,1581],{"className":2715},[622],[568,2717,599],{"className":2718},[622,623],[568,2720,2721,2724],{"style":1259},[568,2722],{"className":2723,"style":1249},[840],[568,2725],{"className":2726,"style":1267},[1266],[568,2728,2729,2732],{"style":1270},[568,2730],{"className":2731,"style":1249},[840],[568,2733,2735],{"className":2734},[622],[568,2736,1180],{"className":2737},[622],[568,2739,1284],{"className":2740},[1283],[568,2742,2744],{"className":2743},[828],[568,2745,2747],{"className":2746,"style":1709},[832],[568,2748],{},[568,2750],{"className":2751},[762,1228],[568,2753],{"className":2754,"style":796},[627],[568,2756,700],{"className":2757},[800],[568,2759],{"className":2760,"style":796},[627],[568,2762,2764,2767,2844,2847,2850],{"className":2763},[613],[568,2765],{"className":2766,"style":2061},[617],[568,2768,2770,2773,2841],{"className":2769},[622],[568,2771],{"className":2772},[734,1228],[568,2774,2776],{"className":2775},[1176],[568,2777,2779,2833],{"className":2778},[824,1235],[568,2780,2782,2830],{"className":2781},[828],[568,2783,2785,2796,2804],{"className":2784,"style":1639},[832],[568,2786,2787,2790],{"style":1245},[568,2788],{"className":2789,"style":1249},[840],[568,2791,2793],{"className":2792},[622],[568,2794,2649],{"className":2795},[622],[568,2797,2798,2801],{"style":1259},[568,2799],{"className":2800,"style":1249},[840],[568,2802],{"className":2803,"style":1267},[1266],[568,2805,2806,2809],{"style":1270},[568,2807],{"className":2808,"style":1249},[840],[568,2810,2812,2815,2818,2821,2824,2827],{"className":2811},[622],[568,2813,1603],{"className":2814},[622],[568,2816],{"className":2817,"style":628},[627],[568,2819,691],{"className":2820},[632],[568,2822],{"className":2823,"style":628},[627],[568,2825,1581],{"className":2826},[622],[568,2828,599],{"className":2829},[622,623],[568,2831,1284],{"className":2832},[1283],[568,2834,2836],{"className":2835},[828],[568,2837,2839],{"className":2838,"style":1291},[832],[568,2840],{},[568,2842],{"className":2843},[762,1228],[568,2845],{"className":2846,"style":796},[627],[568,2848,700],{"className":2849},[800],[568,2851],{"className":2852,"style":796},[627],[568,2854,2856,2860,2863,2871,2875,2878,2881],{"className":2855},[613],[568,2857],{"className":2858,"style":2859},[617],"height:0.8389em;vertical-align:-0.1944em;",[568,2861,914],{"className":2862},[622],[568,2864,2866],{"className":2865},[622],[568,2867,2870],{"className":2868},[2869],"mpunct",",",[568,2872,2874],{"className":2873},[622],"12",[568,2876],{"className":2877,"style":628},[627],[568,2879,691],{"className":2880},[632],[568,2882],{"className":2883,"style":628},[627],[568,2885,2887,2890,2893,2899,2903],{"className":2886},[613],[568,2888],{"className":2889,"style":642},[617],[568,2891,914],{"className":2892},[622],[568,2894,2896],{"className":2895},[622],[568,2897,2870],{"className":2898},[2869],[568,2900,2902],{"className":2901},[622],"16",[568,2904,599],{"className":2905},[622,623],[559,2907,2909],{"id":2908},"typische-fehler","Typische Fehler",[2911,2912,2913,3147,3301],"ul",{},[2914,2915,2916,2917,3146],"li",{},"Realteil durch Realteil und Imaginärteil durch Imaginärteil teilen: ",[568,2918,2920,2965],{"className":2919},[571],[568,2921,2923],{"className":2922},[575],[577,2924,2925],{"xmlns":579},[581,2926,2927,2962],{},[584,2928,2929,2951,2953,2955,2957,2960],{},[1176,2930,2931,2941],{},[584,2932,2933,2935,2937,2939],{},[707,2934,1469],{},[591,2936,593],{},[707,2938,1469],{},[587,2940,599],{},[584,2942,2943,2945,2947,2949],{},[707,2944,1180],{},[591,2946,593],{},[707,2948,709],{},[587,2950,599],{},[591,2952,988],{"mathvariant":987},[707,2954,1469],{},[591,2956,593],{},[707,2958,2959],{},"2,5",[587,2961,599],{},[601,2963,2964],{"encoding":603},"\\frac{5 + 5i}{1 + 2i} \\neq 5 + 2{,}5i",[568,2966,2968,3107,3125],{"className":2967,"ariaHidden":609},[608],[568,2969,2971,2975,3065,3068,3104],{"className":2970},[613],[568,2972],{"className":2973,"style":2974},[617],"height:1.259em;vertical-align:-0.4033em;",[568,2976,2978,2981,3062],{"className":2977},[622],[568,2979],{"className":2980},[734,1228],[568,2982,2984],{"className":2983},[1176],[568,2985,2987,3053],{"className":2986},[824,1235],[568,2988,2990,3050],{"className":2989},[828],[568,2991,2994,3018,3026],{"className":2992,"style":2993},[832],"height:0.8557em;",[568,2995,2997,3000],{"style":2996},"top:-2.655em;",[568,2998],{"className":2999,"style":1249},[840],[568,3001,3003],{"className":3002},[845,846,847,848],[568,3004,3006,3009,3012,3015],{"className":3005},[622,848],[568,3007,1180],{"className":3008},[622,848],[568,3010,593],{"className":3011},[632,848],[568,3013,709],{"className":3014},[622,848],[568,3016,599],{"className":3017},[622,623,848],[568,3019,3020,3023],{"style":1259},[568,3021],{"className":3022,"style":1249},[840],[568,3024],{"className":3025,"style":1267},[1266],[568,3027,3029,3032],{"style":3028},"top:-3.394em;",[568,3030],{"className":3031,"style":1249},[840],[568,3033,3035],{"className":3034},[845,846,847,848],[568,3036,3038,3041,3044,3047],{"className":3037},[622,848],[568,3039,1469],{"className":3040},[622,848],[568,3042,593],{"className":3043},[632,848],[568,3045,1469],{"className":3046},[622,848],[568,3048,599],{"className":3049},[622,623,848],[568,3051,1284],{"className":3052},[1283],[568,3054,3056],{"className":3055},[828],[568,3057,3060],{"className":3058,"style":3059},[832],"height:0.4033em;",[568,3061],{},[568,3063],{"className":3064},[762,1228],[568,3066],{"className":3067,"style":796},[627],[568,3069,3071,3098,3101],{"className":3070},[800],[568,3072,3074],{"className":3073},[800],[568,3075,3077],{"className":3076},[622,1040],[568,3078,3080],{"className":3079},[1044],[568,3081,3083,3086,3095],{"className":3082},[1048],[568,3084],{"className":3085,"style":1021},[617],[568,3087,3089],{"className":3088},[1055],[568,3090,3092],{"className":3091},[622],[568,3093,1062],{"className":3094},[800],[568,3096],{"className":3097},[1066],[568,3099],{"className":3100},[627,1070],[568,3102,700],{"className":3103},[800],[568,3105],{"className":3106,"style":796},[627],[568,3108,3110,3113,3116,3119,3122],{"className":3109},[613],[568,3111],{"className":3112,"style":2154},[617],[568,3114,1469],{"className":3115},[622],[568,3117],{"className":3118,"style":628},[627],[568,3120,593],{"className":3121},[632],[568,3123],{"className":3124,"style":628},[627],[568,3126,3128,3131,3134,3140,3143],{"className":3127},[613],[568,3129],{"className":3130,"style":642},[617],[568,3132,709],{"className":3133},[622],[568,3135,3137],{"className":3136},[622],[568,3138,2870],{"className":3139},[2869],[568,3141,1469],{"className":3142},[622],[568,3144,599],{"className":3145},[622,623],".",[2914,3148,3149,3150,3146],{},"Mit dem Nenner selbst statt mit seiner Konjugierten erweitern. Dann bleibt der Nenner komplex: ",[568,3151,3153,3193],{"className":3152},[571],[568,3154,3156],{"className":3155},[575],[577,3157,3158],{"xmlns":579},[581,3159,3160,3190],{},[584,3161,3162,3164,3166,3168,3170,3172,3178,3180,3182,3184,3186,3188],{},[591,3163,671],{"stretchy":670},[707,3165,1180],{},[591,3167,593],{},[707,3169,709],{},[587,3171,599],{},[702,3173,3174,3176],{},[591,3175,684],{"stretchy":670},[707,3177,709],{},[591,3179,700],{},[591,3181,691],{},[707,3183,1603],{},[591,3185,593],{},[707,3187,1581],{},[587,3189,599],{},[601,3191,3192],{"encoding":603},"(1 + 2i)^2 = -3 + 4i",[568,3194,3196,3217,3268,3289],{"className":3195,"ariaHidden":609},[608],[568,3197,3199,3202,3205,3208,3211,3214],{"className":3198},[613],[568,3200],{"className":3201,"style":730},[617],[568,3203,671],{"className":3204},[734],[568,3206,1180],{"className":3207},[622],[568,3209],{"className":3210,"style":628},[627],[568,3212,593],{"className":3213},[632],[568,3215],{"className":3216,"style":628},[627],[568,3218,3220,3224,3227,3230,3259,3262,3265],{"className":3219},[613],[568,3221],{"className":3222,"style":3223},[617],"height:1.0641em;vertical-align:-0.25em;",[568,3225,709],{"className":3226},[622],[568,3228,599],{"className":3229},[622,623],[568,3231,3233,3236],{"className":3232},[762],[568,3234,684],{"className":3235},[762],[568,3237,3239],{"className":3238},[820],[568,3240,3242],{"className":3241},[824],[568,3243,3245],{"className":3244},[828],[568,3246,3248],{"className":3247,"style":833},[832],[568,3249,3250,3253],{"style":836},[568,3251],{"className":3252,"style":841},[840],[568,3254,3256],{"className":3255},[845,846,847,848],[568,3257,709],{"className":3258},[622,848],[568,3260],{"className":3261,"style":796},[627],[568,3263,700],{"className":3264},[800],[568,3266],{"className":3267,"style":796},[627],[568,3269,3271,3274,3277,3280,3283,3286],{"className":3270},[613],[568,3272],{"className":3273,"style":2154},[617],[568,3275,691],{"className":3276},[622],[568,3278,1603],{"className":3279},[622],[568,3281],{"className":3282,"style":628},[627],[568,3284,593],{"className":3285},[632],[568,3287],{"className":3288,"style":628},[627],[568,3290,3292,3295,3298],{"className":3291},[613],[568,3293],{"className":3294,"style":2173},[617],[568,3296,1581],{"className":3297},[622],[568,3299,599],{"className":3300},[622,623],[2914,3302,3303,3304,3415,3416,3502,3503,3146],{},"Im Nenner ",[568,3305,3307,3333],{"className":3306},[571],[568,3308,3310],{"className":3309},[575],[577,3311,3312],{"xmlns":579},[581,3313,3314,3330],{},[584,3315,3316,3322,3324],{},[702,3317,3318,3320],{},[587,3319,674],{},[707,3321,709],{},[591,3323,691],{},[702,3325,3326,3328],{},[587,3327,679],{},[707,3329,709],{},[601,3331,3332],{"encoding":603},"c^2 - d^2",[568,3334,3336,3380],{"className":3335,"ariaHidden":609},[608],[568,3337,3339,3342,3371,3374,3377],{"className":3338},[613],[568,3340],{"className":3341,"style":810},[617],[568,3343,3345,3348],{"className":3344},[622],[568,3346,674],{"className":3347},[622,623],[568,3349,3351],{"className":3350},[820],[568,3352,3354],{"className":3353},[824],[568,3355,3357],{"className":3356},[828],[568,3358,3360],{"className":3359,"style":833},[832],[568,3361,3362,3365],{"style":836},[568,3363],{"className":3364,"style":841},[840],[568,3366,3368],{"className":3367},[845,846,847,848],[568,3369,709],{"className":3370},[622,848],[568,3372],{"className":3373,"style":628},[627],[568,3375,691],{"className":3376},[632],[568,3378],{"className":3379,"style":628},[627],[568,3381,3383,3386],{"className":3382},[613],[568,3384],{"className":3385,"style":833},[617],[568,3387,3389,3392],{"className":3388},[622],[568,3390,679],{"className":3391},[622,623],[568,3393,3395],{"className":3394},[820],[568,3396,3398],{"className":3397},[824],[568,3399,3401],{"className":3400},[828],[568,3402,3404],{"className":3403,"style":833},[832],[568,3405,3406,3409],{"style":836},[568,3407],{"className":3408,"style":841},[840],[568,3410,3412],{"className":3411},[845,846,847,848],[568,3413,709],{"className":3414},[622,848]," rechnen. Wegen ",[568,3417,3419,3443],{"className":3418},[571],[568,3420,3422],{"className":3421},[575],[577,3423,3424],{"xmlns":579},[581,3425,3426,3440],{},[584,3427,3428,3434,3436,3438],{},[702,3429,3430,3432],{},[587,3431,599],{},[707,3433,709],{},[591,3435,700],{},[591,3437,691],{},[707,3439,1180],{},[601,3441,3442],{"encoding":603},"i^2 = -1",[568,3444,3446,3490],{"className":3445,"ariaHidden":609},[608],[568,3447,3449,3452,3481,3484,3487],{"className":3448},[613],[568,3450],{"className":3451,"style":833},[617],[568,3453,3455,3458],{"className":3454},[622],[568,3456,599],{"className":3457},[622,623],[568,3459,3461],{"className":3460},[820],[568,3462,3464],{"className":3463},[824],[568,3465,3467],{"className":3466},[828],[568,3468,3470],{"className":3469,"style":833},[832],[568,3471,3472,3475],{"style":836},[568,3473],{"className":3474,"style":841},[840],[568,3476,3478],{"className":3477},[845,846,847,848],[568,3479,709],{"className":3480},[622,848],[568,3482],{"className":3483,"style":796},[627],[568,3485,700],{"className":3486},[800],[568,3488],{"className":3489,"style":796},[627],[568,3491,3493,3496,3499],{"className":3492},[613],[568,3494],{"className":3495,"style":2154},[617],[568,3497,691],{"className":3498},[622],[568,3500,1180],{"className":3501},[622]," ist ",[568,3504,3506,3557],{"className":3505},[571],[568,3507,3509],{"className":3508},[575],[577,3510,3511],{"xmlns":579},[581,3512,3513,3555],{},[584,3514,3515,3517,3519,3521,3523,3525,3527,3529,3531,3533,3535,3537,3539,3541,3547,3549],{},[591,3516,671],{"stretchy":670},[587,3518,674],{},[591,3520,593],{},[587,3522,679],{},[587,3524,599],{},[591,3526,684],{"stretchy":670},[591,3528,671],{"stretchy":670},[587,3530,674],{},[591,3532,691],{},[587,3534,679],{},[587,3536,599],{},[591,3538,684],{"stretchy":670},[591,3540,700],{},[702,3542,3543,3545],{},[587,3544,674],{},[707,3546,709],{},[591,3548,593],{},[702,3550,3551,3553],{},[587,3552,679],{},[707,3554,709],{},[601,3556,720],{"encoding":603},[568,3558,3560,3581,3611,3635,3679],{"className":3559,"ariaHidden":609},[608],[568,3561,3563,3566,3569,3572,3575,3578],{"className":3562},[613],[568,3564],{"className":3565,"style":730},[617],[568,3567,671],{"className":3568},[734],[568,3570,674],{"className":3571},[622,623],[568,3573],{"className":3574,"style":628},[627],[568,3576,593],{"className":3577},[632],[568,3579],{"className":3580,"style":628},[627],[568,3582,3584,3587,3590,3593,3596,3599,3602,3605,3608],{"className":3583},[613],[568,3585],{"className":3586,"style":730},[617],[568,3588,679],{"className":3589},[622,623],[568,3591,599],{"className":3592},[622,623],[568,3594,684],{"className":3595},[762],[568,3597,671],{"className":3598},[734],[568,3600,674],{"className":3601},[622,623],[568,3603],{"className":3604,"style":628},[627],[568,3606,691],{"className":3607},[632],[568,3609],{"className":3610,"style":628},[627],[568,3612,3614,3617,3620,3623,3626,3629,3632],{"className":3613},[613],[568,3615],{"className":3616,"style":730},[617],[568,3618,679],{"className":3619},[622,623],[568,3621,599],{"className":3622},[622,623],[568,3624,684],{"className":3625},[762],[568,3627],{"className":3628,"style":796},[627],[568,3630,700],{"className":3631},[800],[568,3633],{"className":3634,"style":796},[627],[568,3636,3638,3641,3670,3673,3676],{"className":3637},[613],[568,3639],{"className":3640,"style":810},[617],[568,3642,3644,3647],{"className":3643},[622],[568,3645,674],{"className":3646},[622,623],[568,3648,3650],{"className":3649},[820],[568,3651,3653],{"className":3652},[824],[568,3654,3656],{"className":3655},[828],[568,3657,3659],{"className":3658,"style":833},[832],[568,3660,3661,3664],{"style":836},[568,3662],{"className":3663,"style":841},[840],[568,3665,3667],{"className":3666},[845,846,847,848],[568,3668,709],{"className":3669},[622,848],[568,3671],{"className":3672,"style":628},[627],[568,3674,593],{"className":3675},[632],[568,3677],{"className":3678,"style":628},[627],[568,3680,3682,3685],{"className":3681},[613],[568,3683],{"className":3684,"style":833},[617],[568,3686,3688,3691],{"className":3687},[622],[568,3689,679],{"className":3690},[622,623],[568,3692,3694],{"className":3693},[820],[568,3695,3697],{"className":3696},[824],[568,3698,3700],{"className":3699},[828],[568,3701,3703],{"className":3702,"style":833},[832],[568,3704,3705,3708],{"style":836},[568,3706],{"className":3707,"style":841},[840],[568,3709,3711],{"className":3710},[845,846,847,848],[568,3712,709],{"className":3713},[622,848],{"title":3715,"searchDepth":3716,"depth":3716,"links":3717},"",2,[3718,3719,3720],{"id":561,"depth":3716,"text":562},{"id":1446,"depth":3716,"text":1447},{"id":2908,"depth":3716,"text":2909},[3722,3725,3728,3730,3733,3735,3737,3740,3742,3744,3747,3750,3753,3755,3757],{"lhs":3723,"rhs":3724},"re(complex(a, b) \u002F complex(c, d))","(a*c + b*d) \u002F (c^2 + d^2)",{"lhs":3726,"rhs":3727},"im(complex(a, b) \u002F complex(c, d))","(b*c - a*d) \u002F (c^2 + d^2)",{"lhs":3729,"rhs":1590},"re((5 + 5*i) * (1 - 2*i))",{"lhs":3731,"rhs":3732},"im((5 + 5*i) * (1 - 2*i))","-5",{"lhs":3734,"rhs":1469},"1^2 + 2^2",{"lhs":3736,"rhs":1603},"re((5 + 5*i) \u002F (1 + 2*i))",{"lhs":3738,"rhs":3739},"im((5 + 5*i) \u002F (1 + 2*i))","-1",{"lhs":3741,"rhs":914},"re(1 \u002F i)",{"lhs":3743,"rhs":3739},"im(1 \u002F i)",{"lhs":3745,"rhs":3746},"re(1 \u002F (3 + 4*i))","0.12",{"lhs":3748,"rhs":3749},"im(1 \u002F (3 + 4*i))","-0.16",{"lhs":3751,"rhs":3752},"re((1 + 2*i)^2)","-3",{"lhs":3754,"rhs":1581},"im((1 + 2*i)^2)",{"lhs":3756,"rhs":3746},"3 \u002F 25",{"lhs":3758,"rhs":3749},"-4 \u002F 25","a, b, c, d \\in \\mathbb{R},\\ c + di \\neq 0","\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 separator=\"true\">,\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>d\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b, c, d \\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=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\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>c\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">c + di \\neq 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\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\">d\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">i\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","complex-division","\\frac{a + bi}{c + di} = \\frac{(a + bi)(c - di)}{c^2 + d^2} = \\frac{ac + bd}{c^2 + d^2} + \\frac{bc - ad}{c^2 + d^2}\\,i","\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>\u003Cmfrac>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>c\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmsup>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>d\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>c\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>d\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmrow>\u003Cmsup>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>d\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>c\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>d\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmrow>\u003Cmsup>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>d\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\frac{a + bi}{c + di} = \\frac{(a + bi)(c - di)}{c^2 + d^2} = \\frac{ac + bd}{c^2 + d^2} + \\frac{bc - ad}{c^2 + d^2}\\,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:2.1408em;vertical-align:-0.7693em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" 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