Roots of Complex Number/Exponential Form/Principal Root

Definition

Let $z := r e^{i \theta}$ be a complex number expressed in exponential form, such that $z \ne 0$.

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

The principal $n$th root of $z$ is the value of $r^{1/n} e^{i \theta / n}$ such that:

$-\pi < \theta \le \pi$

Sources

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of Mathematical Functions ... (previous) ... (next): $3$: Elementary Analytic Methods: $3.7$ Complex Numbers and Functions: Roots: $3.7.28$