Primitive Complex Roots of Unity/Examples/Cube Roots

Examples of Primitive Complex Roots of Unity
The primitive complex cube roots of unity are:

Proof
There are $3$ (complex) cube roots of unity:
 * $1, \omega, \omega^2$

We have:

Also:

Trivially, $1$ is not a primitive complex cube root of unity because you cannot make either $\omega$ or $\omega^2$ by multiplying $1$ by itself as many times as you like.

Hence the result.