x^2=1184+125.6637i

解

x^{2} = 1184 + 125.6637 i

x = \frac{11840000 + 1.41765 E 14}{100 2} + \frac{6283.185 2}{11840000 + 1.41765 E 14} i, x = - \frac{11840000 + 1.41765 E 14}{100 2} - \frac{2 \cdot 6283.185}{11840000 + 1.41765 E 14} i

解答ステップ

x^{2} = 1184 + 125.6637 i

代用

x = a + bi

(a + bi)^{2} = 1184 + 125.6637 i

拡張

(a + bi)^{2} : (a^{2} - b^{2}) + 2 iab

(a^{2} - b^{2}) + 2 iab = 1184 + 125.6637 i

複素数は, その実数部と虚数部が等しい場合にのみ等しくなるequation系として書き換える:

[a^{2} - b^{2} = 1184 2 ab = 125.6637]

[a^{2} - b^{2} = 1184 2 ab = 125.6637] : a = \frac{11840000 + 1.41765 E 14}{100 2}, a = - \frac{11840000 + 1.41765 E 14}{100 2}, b = \frac{6283.185 2}{11840000 + 1.41765 E 14} b = - \frac{2 \cdot 6283.185}{11840000 + 1.41765 E 14}

代用を戻す

x = a + bi

x = \frac{11840000 + 1.41765 E 14}{100 2} + \frac{6283.185 2}{11840000 + 1.41765 E 14} i, x = - \frac{11840000 + 1.41765 E 14}{100 2} - \frac{2 \cdot 6283.185}{11840000 + 1.41765 E 14} i