(x+iy)^2-2(x-iy)=0

解

(x + i y)^{2} - 2 (x - i y) = 0

x = 2, x = 0, x = - 1, x = - 1, y = 0 y = 0 y = 3 y = - 3

解答ステップ

(x + i y)^{2} - 2 (x - i y) = 0

拡張

(x + i y)^{2} - 2 (x - i y) : (x^{2} - y^{2} - 2 x) + i (2 y + 2 x y)

(x^{2} - y^{2} - 2 x) + i (2 y + 2 x y) = 0

標準的な複素数形式で

0

を書き換える:

0 + 0 i

(x^{2} - y^{2} - 2 x) + i (2 y + 2 x y) = 0 + 0 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:

[x^{2} - y^{2} - 2 x = 0 2 y + 2 x y = 0]

[x^{2} - y^{2} - 2 x = 0 2 y + 2 x y = 0] : x = 2, x = 0, x = - 1, x = - 1, y = 0 y = 0 y = 3 y = - 3

x = 2, x = 0, x = - 1, x = - 1, y = 0 y = 0 y = 3 y = - 3