solvefor z,z^2=(x+iy)^2

解

解く

z, z^{2} = (x + i y)^{2}

z = x + y i, z = - x - y i, z = - y^{2} + \frac{x y}{- y ^{2}} i, z = - - y^{2} - \frac{x y}{- y ^{2}} i

解答ステップ

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

代用

z = x + y i

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

拡張

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

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

代用を戻す

z = x + y i

z = x + y i, z = - x - y i, z = - y^{2} + \frac{x y}{- y ^{2}} i, z = - - y^{2} - \frac{x y}{- y ^{2}} i