What is the answer to (x+iy-1)^2=(x+iy-i)^2 ?

The answer to (x+iy-1)^2=(x+iy-i)^2 is

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(x+iy-1)^2=(x+iy-i)^2

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

(x = \frac{1}{2}, y = \frac{1}{2})

Solution steps

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

Expand

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

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

[x^{2} - 2 x - y^{2} + 1 = x^{2} - 1 - y^{2} + 2 y - 2 y + 2 x y = - 2 x + 2 x y]

[x^{2} - 2 x - y^{2} + 1 = x^{2} - 1 - y^{2} + 2 y - 2 y + 2 x y = - 2 x + 2 x y] : (x = \frac{1}{2}, y = \frac{1}{2})

(x = \frac{1}{2}, y = \frac{1}{2})

(7 a + bi) + (- 3 b + ai) = (2 + 5 i)

(x + y i)^{2} = - 5 + 12 i

z^{2} - 7 z + 13 = i

2 z^{2} + 4 z + 1 - i 3 = 0

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

What is the answer to (x+iy-1)^2=(x+iy-i)^2 ?
The answer to (x+iy-1)^2=(x+iy-i)^2 is