# Roots of Complex Number/Corollary/Examples/Cube Roots

## Example of Roots of Complex Number: Corollary

Let $z \in \C$ be a complex number.

Let $z \ne 0$.

Let $w$ be one of the (complex) cube roots of $z$.

Then the complete set of (complex) cube roots of $z$ is:

$\set {w, w \omega, w \omega^2}$

where:

$\omega = e^{2 \pi / 3} = -\dfrac 1 2 + \dfrac {i \sqrt 3} 2$

## Proof

From Primitive Complex Cube Roots of Unity, $\omega$ is a primitive root of $1$.

Hence the result from Roots of Complex Number: Corollary.

$\blacksquare$