What is the answer to x^2=4+4sqrt(15)i ?

The answer to x^2=4+4sqrt(15)i is x=sqrt(10)+sqrt(6)i,x=-sqrt(10)-sqrt(6)i

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x^2=4+4sqrt(15)i

x^{2} = 4 + 415 i

x = 10 + 6 i, x = - 10 - 6 i

Solution steps

x^{2} = 4 + 415 i

Substitute

x = a + bi

(a + bi)^{2} = 4 + 415 i

Expand

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

(a^{2} - b^{2}) + 2 iab = 4 + 415 i

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

[a^{2} - b^{2} = 4 2 ab = 415]

[a^{2} - b^{2} = 4 2 ab = 415] : (a = 10, a = - 10, b = 6 b = - 6)

Substitute back

x = a + bi

x = 10 + 6 i, x = - 10 - 6 i

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

z^{2} + 4 i z - 1 = 0

c, z = \frac{- 3 + 3 i}{2 - c}

z^{2} = - 15 + 8 i

\frac{( - 6 i + n - 3 n + 5 )}{4 + n ^{2}} = 0

What is the answer to x^2=4+4sqrt(15)i ?
The answer to x^2=4+4sqrt(15)i is x=sqrt(10)+sqrt(6)i,x=-sqrt(10)-sqrt(6)i