# Definition:Complex Root

## Definition

Let $z \in \C$ be a complex number such that $z \ne 0$.

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

Let $w \in \C$ such that:

$w^n = z$

Then $w$ is a (complex) $n$th root of $z$, and we can write:

$w = z^{1 / n}$

## Also see

• Roots of Complex Number, where it is demonstrated what the complex $n$th roots actually are in terms of $z$ and $n$.