Definition:Principal Square Root/Also defined as

Definition

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

Let $z^{1/2} = \set {w \in \C: w^2 = z}$ be the square root of $z$.

The principal square root of $z$ can sometimes also be found defined as the element $w$ of $z^{1/2}$ such that:

$0 \le \arg w < \pi$