What is the answer to (x+iy)^2+2(x-iy)=2(x+iy) ?

The answer to (x+iy)^2+2(x-iy)=2(x+iy) is

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

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

x = 0, x = 2, x = 2, y = 0 y = 2 y = - 2

Solution steps

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

Expand

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

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

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

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

x = 0, x = 2, x = 2, y = 0 y = 2 y = - 2

x^{2} - 8.4 x i - 3.15 = 0

z^{2} + (2 - 12 i) z + (- 1 - 9 i) = 0

x, s i g = \frac{2}{x - 3}

z^{2} (1 + i) = 2 i

z = z + \frac{i}{z}

What is the answer to (x+iy)^2+2(x-iy)=2(x+iy) ?
The answer to (x+iy)^2+2(x-iy)=2(x+iy) is