What are the solutions to the equation z^5=-i ?

The solutions to the equation z^5=-i are

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z^5=-i

z^{5} = - i

z = \frac{2 5 + 5}{4} - i \frac{2 3 - 5}{4}, z = \frac{10 - 2 5}{4} + i \frac{1 + 5}{4}, z = - \frac{10 - 2 5}{4} + i \frac{1 + 5}{4}, z = - \frac{2 5 + 5}{4} - i \frac{2 3 - 5}{4}, z = - i

Solution steps

z^{5} = - i

For

z^{n} = a

the solutions are

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

For

n = 5, a = - i

∣ a ∣ = 1

ar g (a) = - \frac{π}{2}

Simplify

z = \frac{2 5 + 5}{4} - i \frac{2 3 - 5}{4}, z = \frac{10 - 2 5}{4} + i \frac{1 + 5}{4}, z = - \frac{10 - 2 5}{4} + i \frac{1 + 5}{4}, z = - \frac{2 5 + 5}{4} - i \frac{2 3 - 5}{4}, z = - i

x^{2} (x - 5) + 5 - x = 0

x^{4} + x^{3} - 6 x^{2} + 7 x + 49 = 0

x^{4} - 1 3^{2} + 36 = 0

x^{3} + x^{2} - 26 x + 24 = 0

x^{2} (- x + 1) + x - 1 = 0

What are the solutions to the equation z^5=-i ?
The solutions to the equation z^5=-i are
Find the zeros of z^5=-i
The zeros of z^5=-i are