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 $z$ for $\map \Im z = 0$ can also be reported as:
 * $w \ge 0$

as in this case $w$ is wholly real.