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

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

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x+yi=(1-i)^2

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

x = 0, y = - 2

Solution steps

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

Expand

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

x + y i = - 2 i

Rewrite

- 2 i

in standard complex form:

0 - 2 i

x + y i = 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

\frac{1 + z}{1 - z} = 8 i - 5

\frac{1 + 2 z}{3 + 2 z} = i

\frac{- 1}{b + i} = \frac{1}{- b + i}

(x + y) + (x - y) \cdot i = 2 + 5 \cdot i

(1 + i) (x + y i) = 1 + 3 i