What is the answer to x^2=-4i ?

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

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x^2=-4i

x^{2} = - 4 i

x = 2 - 2 i, x = - 2 + 2 i

Solution steps

x^{2} = - 4 i

Substitute

x = a + bi

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

Expand

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

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

Rewrite

- 4 i

in standard complex form:

0 - 4 i

(a^{2} - b^{2}) + 2 iab = 0 - 4 i

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

[a^{2} - b^{2} = 0 2 ab = - 4]

[a^{2} - b^{2} = 0 2 ab = - 4] : (a = 2, a = - 2, b = - 2 b = 2)

Substitute back

x = a + bi

x = 2 - 2 i, x = - 2 + 2 i

(a + bi)^{2} = 1

25 x^{2} + 60 x + 37 = 0 a + bi

z^{2} - (2 + i 3) z - 5 + i = 0

x^{2} + 4 i \cdot x - 1 = 0

a \cdot (a - bi) = 4 + 6 i

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