De Moivre's Theorem

De Moivre’s theorem is used for powers of a complex number, when the complex number is represented using polar form or the complex exponential.

Definition §

Let $z$ be a complex number, $z\in \mathbb{C}$ , in its polar form: $z=r\text{cis}(\theta )=r{e}^{i\theta }$. Then:

In other words, a complex number raised to a power is equal to magnitude raised to the power times the product of the angle.