Definition:Square Root/Complex Number/Definition 3

Definition
Let $z \in \C$ be a complex number.

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


 * $z^{1/2} = \left\{ {\sqrt {\left\vert{z}\right\vert} e^{\left({i / 2}\right) \arg \left({z}\right)} }\right\}$

where:
 * $\sqrt {\left\vert{z}\right\vert}$ denotes the positive square root of the complex modulus of $z$
 * $\arg \left({z}\right)$ denotes the argument of $z$ considered as a multifunction.

Also see

 * Equivalence of Definitions of Square Root of Complex Number