Definition:Square Root/Complex Number/Definition 2

Definition
Let $z \in \C$ be a complex number expressed in polar form as $\left \langle{r, \theta}\right\rangle = r \left({\cos \theta + i \sin \theta}\right)$.

The square root of $z$ is the $2$-valued multifunction:


 * $z^{1/2} = \left\{ {\pm \sqrt r \left({\cos \left({\dfrac \theta 2}\right) + i \sin \left({\dfrac \theta 2}\right) }\right)}\right\}$

where $\pm \sqrt r$ denotes the positive and negative square roots of $r$.

Also see

 * Equivalence of Definitions of Square Root of Complex Number