What is the answer to (x-yi)^2=9(x+yi) ?

The answer to (x-yi)^2=9(x+yi) is

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(x-yi)^2=9(x+yi)

(x - y i)^{2} = 9 (x + y i)

x = 9, x = 0, x = - \frac{9}{2}, x = - \frac{9}{2}, y = 0 y = 0 y = \frac{9 3}{2} y = - \frac{9 3}{2}

Solution steps

(x - y i)^{2} = 9 (x + y i)

Expand

(x^{2} - y^{2}) - 2 i x y = 9 x + 9 i y

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

[x^{2} - y^{2} = 9 x - 2 x y = 9 y]

[x^{2} - y^{2} = 9 x - 2 x y = 9 y] : x = 9, x = 0, x = - \frac{9}{2}, x = - \frac{9}{2}, y = 0 y = 0 y = \frac{9 3}{2} y = - \frac{9 3}{2}

x = 9, x = 0, x = - \frac{9}{2}, x = - \frac{9}{2}, y = 0 y = 0 y = \frac{9 3}{2} y = - \frac{9 3}{2}

\frac{2 + i}{1 + i} = a + bi

x^{2} - (2 + 3 i) = 0

2 x^{2} - 2 i x - 1 = 0

\frac{- 4 + mi}{2 - 3 i} = n - 2 i

3 x + y + (2 x + 2 y) i = 13