What is the answer to (x+yi)^2=2+2isqrt(3) ?

The answer to (x+yi)^2=2+2isqrt(3) is

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(x+yi)^2=2+2isqrt(3)

(x + y i)^{2} = 2 + 2 i 3

(x = 3, x = - 3, y = 1 y = - 1)

Solution steps

(x + y i)^{2} = 2 + 2 i 3

Expand

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

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

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

[x^{2} - y^{2} = 2 2 x y = 23]

[x^{2} - y^{2} = 2 2 x y = 23] : (x = 3, x = - 3, y = 1 y = - 1)

(x = 3, x = - 3, y = 1 y = - 1)

- 3 + y i = x + 6 i

40 - w^{2} - 2 w \cdot i = 0

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

\frac{2 x}{1 + x - y i} = 3 - 4 i

12 i + 12 y i^{2} = - 24 x i + 6

What is the answer to (x+yi)^2=2+2isqrt(3) ?
The answer to (x+yi)^2=2+2isqrt(3) is