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

The answer to x+iy=(1-i)^2 is x=0,y=-2

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x+iy=(1-i)^2

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

x = 0, y = - 2

Solution steps

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

Expand

(1 - i)^{2} : - 2 i

x + i y = - 2 i

Rewrite

- 2 i

in standard complex form:

0 - 2 i

x + i y = 0 - 2 i

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

[x = 0 y = - 2]

[x = 0 y = - 2] : x = 0, y = - 2

x = 0, y = - 2

(1 + 2 i) (x + y i) - (1 + 2 i) (x - y i) = 16

z^{2} = - 4 i

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

(x + y i) (2 + i) = 3 - i

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