What is the answer to x^2=-2-2sqrt(3)i ?

The answer to x^2=-2-2sqrt(3)i is x=1-sqrt(3)i,x=-1+sqrt(3)i

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x^2=-2-2sqrt(3)i

x^{2} = - 2 - 23 i

x = 1 - 3 i, x = - 1 + 3 i

Solution steps

x^{2} = - 2 - 23 i

Substitute

x = a + bi

(a + bi)^{2} = - 2 - 23 i

Expand

(a + bi)^{2} : (a^{2} - b^{2}) + 2 iab

(a^{2} - b^{2}) + 2 iab = - 2 - 23 i

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

[a^{2} - b^{2} = - 2 2 ab = - 23]

[a^{2} - b^{2} = - 2 2 ab = - 23] : (a = 1, a = - 1, b = - 3 b = 3)

Substitute back

x = a + bi

x = 1 - 3 i, x = - 1 + 3 i

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

z^{2} + 2 i z - 1 = 0

(a + i)^{2} = 8 - 6 i

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

(x + 4 i) (x - 4 i) = 0

What is the answer to x^2=-2-2sqrt(3)i ?
The answer to x^2=-2-2sqrt(3)i is x=1-sqrt(3)i,x=-1+sqrt(3)i