What is the answer to (3+4i)^2-2(x-iy)=x+iy ?

The answer to (3+4i)^2-2(x-iy)=x+iy is x=-7/3 ,y=-24

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(3+4i)^2-2(x-iy)=x+iy

(3 + 4 i)^{2} - 2 (x - i y) = x + i y

x = - \frac{7}{3}, y = - 24

Solution steps

(3 + 4 i)^{2} - 2 (x - i y) = x + i y

Expand

(3 + 4 i)^{2} - 2 (x - i y) : (- 7 - 2 x) + i (24 + 2 y)

(- 7 - 2 x) + i (24 + 2 y) = x + i y

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

[- 7 - 2 x = x 24 + 2 y = y]

[- 7 - 2 x = x 24 + 2 y = y] : x = - \frac{7}{3}, y = - 24

x = - \frac{7}{3}, y = - 24

3 x - y - i = 2 i x - i y

x^{2} - 8 i x - 25 = 0

- 4 + (y) i = - 12 x - i + 8

z^{2} - (3 + 5 i) z + 8 i - 5 = 0

z^{2} + 2 z = 6 - 24 i

What is the answer to (3+4i)^2-2(x-iy)=x+iy ?
The answer to (3+4i)^2-2(x-iy)=x+iy is x=-7/3 ,y=-24