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

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

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z^6=-i

z^{6} = - i

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

Solution steps

z^{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

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

2 y^{4} + y^{2} = 36

2 x^{3} - 3 x^{2} + 16 x - 24 = 0

y^{3} - 3 y^{2} + 3 y - 1 = 0

x^{4} + 4 x^{2} - 32 = 0

- a^{3} + 4 a^{2} - 3 a = 0

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