Definition:Square Root/Complex Number/Definition 1

Definition
Let $z \in \C$ be a complex number expressed in polar form as $\polar {r, \theta} = r \paren {\cos \theta + i \sin \theta}$.

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

where $\sqrt r$ denotes the positive square root of $r$.

Also see

 * Equivalence of Definitions of Square Root of Complex Number