(x+iy)^2=3+2i

解

(x + i y)^{2} = 3 + 2 i

x = \frac{13 + 3}{2}, x = - \frac{13 + 3}{2}, y = \frac{13 - 3}{2} y = - \frac{13 - 3}{2}

解答ステップ

(x + i y)^{2} = 3 + 2 i

拡張

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

(x^{2} - y^{2}) + 2 i x y = 3 + 2 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} = 3 2 x y = 2]

[x^{2} - y^{2} = 3 2 x y = 2] : x = \frac{13 + 3}{2}, x = - \frac{13 + 3}{2}, y = \frac{13 - 3}{2} y = - \frac{13 - 3}{2}

x = \frac{13 + 3}{2}, x = - \frac{13 + 3}{2}, y = \frac{13 - 3}{2} y = - \frac{13 - 3}{2}