What is the answer to (x-iy)^2=4(x+iy) ?

The answer to (x-iy)^2=4(x+iy) is

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(x-iy)^2=4(x+iy)

(x - i y)^{2} = 4 (x + i y)

x = 4, x = 0, x = - 2, x = - 2, y = 0 y = 0 y = 23 y = - 23

Solution steps

(x - i y)^{2} = 4 (x + i y)

Expand

(x^{2} - y^{2}) - 2 i x y = 4 x + 4 i y

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

[x^{2} - y^{2} = 4 x - 2 x y = 4 y]

[x^{2} - y^{2} = 4 x - 2 x y = 4 y] : x = 4, x = 0, x = - 2, x = - 2, y = 0 y = 0 y = 23 y = - 23

x = 4, x = 0, x = - 2, x = - 2, y = 0 y = 0 y = 23 y = - 23

z^{2} + (2 i - 3) z + 5 - i = 0

z^{2} - (5 - 4 i) z + (3 - 11 i) = 0

z^{2} + 2 \cdot i \cdot z - 1 - i = 0

x^{2} - 2 (1 + i) x + (2 i - 1) = 0

(x + i y) (3 + i) = 5