Complex Roots of Unity/Examples/Cube Roots/Conjugate Form

Example of Complex Roots of Unity
The Cube Roots of Unity can be expressed in the form:
 * $U_3 = \set {1, \omega, \overline \omega}$

where:
 * $\omega = -\dfrac 1 2 + \dfrac {i \sqrt 3} 2$
 * $\overline \omega$ denotes the complex conjugate of $\omega$.

Proof
We have that the Cube Roots of Unity can be expressed as:
 * $U_3 = \set {1, \omega, \omega^2}$

Then: