(x-yi)^2=9(x+yi)

解

(x - y i)^{2} = 9 (x + y i)

x = 9, x = 0, x = - \frac{9}{2}, x = - \frac{9}{2}, y = 0 y = 0 y = \frac{9 3}{2} y = - \frac{9 3}{2}

解答ステップ

(x - y i)^{2} = 9 (x + y i)

拡張

(x^{2} - y^{2}) - 2 i x y = 9 x + 9 i y

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:

[x^{2} - y^{2} = 9 x - 2 x y = 9 y]

[x^{2} - y^{2} = 9 x - 2 x y = 9 y] : x = 9, x = 0, x = - \frac{9}{2}, x = - \frac{9}{2}, y = 0 y = 0 y = \frac{9 3}{2} y = - \frac{9 3}{2}

x = 9, x = 0, x = - \frac{9}{2}, x = - \frac{9}{2}, y = 0 y = 0 y = \frac{9 3}{2} y = - \frac{9 3}{2}