What are the solutions to the equation z^4=-2-2sqrt(3)i ?

The solutions to the equation z^4=-2-2sqrt(3)i are

Find the zeros of z^4=-2-2sqrt(3)i

The zeros of z^4=-2-2sqrt(3)i are

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z^{4} = - 2 - 23 i

z = \frac{3}{2} - i \frac{2}{2}, z = \frac{2}{2} + i \frac{3}{2}, z = - \frac{3}{2} + i \frac{2}{2}, z = - \frac{2}{2} - i \frac{3}{2}

Solution steps

z^{4} = - 2 - 23 i

For

z^{n} = a

the solutions are

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

For

n = 4, a = - 2 - 23 i

∣ a ∣ = 4

ar g (a) = \frac{π}{3} - π

Simplify

z = \frac{3}{2} - i \frac{2}{2}, z = \frac{2}{2} + i \frac{3}{2}, z = - \frac{3}{2} + i \frac{2}{2}, z = - \frac{2}{2} - i \frac{3}{2}

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

x^{4} + x = 0

z^{4} + 1 - i 3 = 0

3 x^{3} + x^{2} - 12 x - 4 = 0

x^{3} + 9 x = 0

What are the solutions to the equation z^4=-2-2sqrt(3)i ?
The solutions to the equation z^4=-2-2sqrt(3)i are
Find the zeros of z^4=-2-2sqrt(3)i
The zeros of z^4=-2-2sqrt(3)i are