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

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

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

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

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

Solution steps

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

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

x^{2} + i x + 2 = 0

3 (x + 5 i) = 7 y i - 6 + 8

x - 5 i + 2 = 4 - 3 i + y i

(x + y i) + (4 + 9 i) = 9 - 4 i

x - i y = 3 + 4 i