What are the solutions to the equation x^8=-256 ?

The solutions to the equation x^8=-256 are

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x^8=-256

x^{8} = - 256

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

Solution steps

x^{8} = - 256

Rewrite the equation with

u = x^{2}

and

u^{4} = x^{8}

u^{4} = - 256

Solve

u^{4} = - 256 : u = 22 + 22 i, u = - 22 - 22 i, u = - 22 + 22 i, u = 22 - 22 i

u = 22 + 22 i, u = - 22 - 22 i, u = - 22 + 22 i, u = 22 - 22 i

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 22 + 22 i : x = 2 + 2 + 2 - 2 i, x = - 2 + 2 - 2 - 2 i

Solve

x^{2} = - 22 - 22 i : x = - 2 - 2 + 2 + 2 i, x = 2 - 2 - 2 + 2 i

Solve

x^{2} = - 22 + 22 i : x = 2 - 2 + 2 + 2 i, x = - 2 - 2 - 2 + 2 i

Solve

x^{2} = 22 - 22 i : x = - 2 + 2 + 2 - 2 i, x = 2 + 2 - 2 - 2 i

The solutions are

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

x^{4} - 4 x^{3} + 4 x^{2}

(x^{2} - 36)^{2} + (x^{2} + 4 x - 12)^{2} = 0

4 x^{3} + 6 x^{2} - 72 x - 3 = 0

2 x^{3} - 16 x^{2} - 40 x = 0

z^{5} + i = 0

What are the solutions to the equation x^8=-256 ?
The solutions to the equation x^8=-256 are
Find the zeros of x^8=-256
The zeros of x^8=-256 are