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:


 * $z^{1/2} = \set {\sqrt {\cmod z} \, e^{\paren {i / 2} \map \arg z} }$

where:
 * $\sqrt {\cmod z}$ denotes the positive square root of the complex modulus of $z$
 * $\map \arg z$ denotes the argument of $z$ considered as a multifunction.

Also see

 * Equivalence of Definitions of Square Root of Complex Number