What are the solutions to the equation z^4=-8sqrt(3)+8i ?

The solutions to the equation z^4=-8sqrt(3)+8i are

Find the zeros of z^4=-8sqrt(3)+8i

The zeros of z^4=-8sqrt(3)+8i are

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z^{4} = - 83 + 8 i

z = \frac{4 - 2 + 6}{2} + i \frac{4 + 2 - 6}{2}, z = - \frac{4 + 2 - 6}{2} + i \frac{4 - 2 + 6}{2}, z = - \frac{4 - 2 + 6}{2} - i \frac{4 + 2 - 6}{2}, z = \frac{4 + 2 - 6}{2} - i \frac{4 - 2 + 6}{2}

Solution steps

z^{4} = - 83 + 8 i

For

z^{n} = a

the solutions are

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

For

n = 4, a = - 83 + 8 i

∣ a ∣ = 16

ar g (a) = - \frac{π}{6} + π

Simplify

z = \frac{4 - 2 + 6}{2} + i \frac{4 + 2 - 6}{2}, z = - \frac{4 + 2 - 6}{2} + i \frac{4 - 2 + 6}{2}, z = - \frac{4 - 2 + 6}{2} - i \frac{4 + 2 - 6}{2}, z = \frac{4 + 2 - 6}{2} - i \frac{4 - 2 + 6}{2}

2 = \frac{4}{3} π r^{3}

16 x^{4} = 1

1500 = 986 (1 + x)^{3}

x^{6} + 2 x^{3} + 2 = 0

x^{4} - 3 x^{3} - 5 x^{2} + 13 x + 6 = 0

What are the solutions to the equation z^4=-8sqrt(3)+8i ?
The solutions to the equation z^4=-8sqrt(3)+8i are
Find the zeros of z^4=-8sqrt(3)+8i
The zeros of z^4=-8sqrt(3)+8i are