Definition:Root of Unity/Complex/First

Definition
Let $n \in \Z_{>0}$ be a (strictly) positive integer.

In Complex Roots of Unity in Exponential Form it is shown that the complex $n$th roots of unity are the elements of the set:
 * $U_n = \set {e^{2 i k \pi / n}: k \in \N_n}$

The root $e^{2 i \pi / n}$ is known as the first (complex) $n$th root of unity.

Notation
The first $n$th root of unity is usually assigned a letter of the Greek alphabet: $\alpha$, $\epsilon$, $\omega$.

intends to use $\alpha$ as standard.

Many texts reserve $\omega$ for the first complex cube root of unity:
 * $\omega = -\dfrac 1 2 + i \dfrac {\sqrt 3} 2$

which convention is adopted by.