What are the solutions to the equation -i=x^6 ?

The solutions to the equation -i=x^6 are

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-i=x^6

- i = x^{6}

x = \frac{2 ( 1 + 3 )}{4} + i \frac{2 ( 1 - 3 )}{4}, x = \frac{2}{2} + i \frac{2}{2}, x = \frac{2 ( 1 - 3 )}{4} + i \frac{2 ( 1 + 3 )}{4}, x = \frac{2 ( - 1 - 3 )}{4} + i \frac{2 ( - 1 + 3 )}{4}, x = - \frac{2}{2} - i \frac{2}{2}, x = \frac{2 ( - 1 + 3 )}{4} + i \frac{2 ( - 1 - 3 )}{4}

Solution steps

- i = x^{6}

Switch sides

x^{6} = - i

For

z^{n} = a

the solutions are

k = 0, 1, \dots, n - 1

For

n = 6, a = - i

∣ a ∣ = 1

ar g (a) = - \frac{π}{2}

Simplify

x = \frac{2 ( 1 + 3 )}{4} + i \frac{2 ( 1 - 3 )}{4}, x = \frac{2}{2} + i \frac{2}{2}, x = \frac{2 ( 1 - 3 )}{4} + i \frac{2 ( 1 + 3 )}{4}, x = \frac{2 ( - 1 - 3 )}{4} + i \frac{2 ( - 1 + 3 )}{4}, x = - \frac{2}{2} - i \frac{2}{2}, x = \frac{2 ( - 1 + 3 )}{4} + i \frac{2 ( - 1 - 3 )}{4}

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

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

z^{3} + i = 0

x^{4} - 2 x^{2} - 63 = 0

3 x - 2 = x^{8}

What are the solutions to the equation -i=x^6 ?
The solutions to the equation -i=x^6 are
Find the zeros of -i=x^6
The zeros of -i=x^6 are