What are the solutions to the equation z^3=-1-i ?

The solutions to the equation z^3=-1-i are

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z^3=-1-i

z^{3} = - 1 - i

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

Solution steps

z^{3} = - 1 - i

For

z^{n} = a

the solutions are

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

For

n = 3, a = - 1 - i

∣ a ∣ = 2

ar g (a) = \frac{π}{4} - π

Simplify

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

x^{2} (x + 3) = 0

y, (y - x)^{3} = C x

x^{3} + 3 x^{2} - 36 x - 108 = 0

17 + x^{3} = x^{2} + 17

4 x^{3} = 32

What are the solutions to the equation z^3=-1-i ?
The solutions to the equation z^3=-1-i are
Find the zeros of z^3=-1-i
The zeros of z^3=-1-i are