What is the answer to w^2-i(w-2)=(w-2) ?

The answer to w^2-i(w-2)=(w-2) is w=2i,w=1-i

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w^2-i(w-2)=(w-2)

w^{2} - i (w - 2) = (w - 2)

w = 2 i, w = 1 - i

Solution steps

w^{2} - i (w - 2) = (w - 2)

Substitute

w = x + y i

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

Expand

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

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

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

[x^{2} - y^{2} + y = x - 2 2 - x + 2 x y = y] : (x = 0, x = 1, y = 2 y = - 1)

Substitute back

w = x + y i

w = 2 i, w = 1 - i

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

\frac{- 4 + x i}{2 - 3 i} = y - 2 i

3 x - 2 i y - i x + 5 y = 7 + 5 i

x + i y = ∣ x - i y ∣

\frac{4 + x i}{2 + i} = y + 2 i

What is the answer to w^2-i(w-2)=(w-2) ?
The answer to w^2-i(w-2)=(w-2) is w=2i,w=1-i