What is the answer to x^2+8i=0 ?

The answer to x^2+8i=0 is x=2-2i,x=-2+2i

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x^2+8i=0

x^{2} + 8 i = 0

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

Solution steps

x^{2} + 8 i = 0

Substitute

x = a + bi

(a + bi)^{2} + 8 i = 0

Expand

(a + bi)^{2} + 8 i : (a^{2} - b^{2}) + i (8 + 2 ab)

(a^{2} - b^{2}) + i (8 + 2 ab) = 0

Rewrite

0

in standard complex form:

0 + 0 i

(a^{2} - b^{2}) + i (8 + 2 ab) = 0 + 0 i

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

[a^{2} - b^{2} = 0 8 + 2 ab = 0]

[a^{2} - b^{2} = 0 8 + 2 ab = 0] : (a = 2, a = - 2, b = - 2 b = 2)

Substitute back

x = a + bi

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

2 i x^{2} + x + 3 i = 0

w^{2} - i (w - 2) = (w - 2)

x^{2} - y^{2} + i 2 x y = y + i x

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

3 x - 2 i y - i x + 5 y = 7 + 5 i