What are the solutions to the equation z^3=-27i ?

The solutions to the equation z^3=-27i are z=(3sqrt(3))/2-i 3/2 ,z=3i,z=-(3sqrt(3))/2-i 3/2

Find the zeros of z^3=-27i

The zeros of z^3=-27i are z=(3sqrt(3))/2-i 3/2 ,z=3i,z=-(3sqrt(3))/2-i 3/2

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z^{3} = - 27 i

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

Solution steps

z^{3} = - 27 i

For

z^{n} = a

the solutions are

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

For

n = 3, a = - 27 i

∣ a ∣ = 27

ar g (a) = - \frac{π}{2}

Simplify

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

x^{3} - 2 = 0

x^{3} - 6 x^{2} + 8 x = 0

x^{3} - 5 x^{2} + 5 x - 25 = 0

- x^{3} + 13 x^{2} - 56 x + 80 = 0

z^{3} - 27 = 0

What are the solutions to the equation z^3=-27i ?
The solutions to the equation z^3=-27i are z=(3sqrt(3))/2-i 3/2 ,z=3i,z=-(3sqrt(3))/2-i 3/2
Find the zeros of z^3=-27i
The zeros of z^3=-27i are z=(3sqrt(3))/2-i 3/2 ,z=3i,z=-(3sqrt(3))/2-i 3/2