What are the solutions to the equation z^4=4i ?

The solutions to the equation z^4=4i are

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z^4=4i

z^{4} = 4 i

z = \frac{2 + 2}{2} + i \frac{2 - 2}{2}, z = - \frac{2 - 2}{2} + i \frac{2 + 2}{2}, z = - \frac{2 + 2}{2} - i \frac{2 - 2}{2}, z = \frac{2 - 2}{2} - i \frac{2 + 2}{2}

Solution steps

z^{4} = 4 i

For

z^{n} = a

the solutions are

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

For

n = 4, a = 4 i

∣ a ∣ = 4

ar g (a) = \frac{π}{2}

Simplify

z = \frac{2 + 2}{2} + i \frac{2 - 2}{2}, z = - \frac{2 - 2}{2} + i \frac{2 + 2}{2}, z = - \frac{2 + 2}{2} - i \frac{2 - 2}{2}, z = \frac{2 - 2}{2} - i \frac{2 + 2}{2}

r^{3} - 5 r^{2} + 8 r - 4 = 0

x^{3} - 3 x^{2} + 5 x - 4 = 0

x^{3} - 6 x + 9 = 0

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

12 x^{3} - 5 x + 132 = 0

What are the solutions to the equation z^4=4i ?
The solutions to the equation z^4=4i are
Find the zeros of z^4=4i
The zeros of z^4=4i are