(a-bi)^2=13-12i

解

(a - bi)^{2} = 13 - 12 i

a = \frac{6 2}{313 - 13}, a = - \frac{6 2}{313 - 13}, b = \frac{313 - 13}{2} b = - \frac{313 - 13}{2}

解答ステップ

(a - bi)^{2} = 13 - 12 i

拡張

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

(a^{2} - b^{2}) - 2 iab = 13 - 12 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} = 13 - 2 ab = - 12]

[a^{2} - b^{2} = 13 - 2 ab = - 12] : a = \frac{6 2}{313 - 13}, a = - \frac{6 2}{313 - 13}, b = \frac{313 - 13}{2} b = - \frac{313 - 13}{2}

a = \frac{6 2}{313 - 13}, a = - \frac{6 2}{313 - 13}, b = \frac{313 - 13}{2} b = - \frac{313 - 13}{2}