Definition:Argument of Complex Number/Principal Range

Definition
It is understood that the argument of a complex number $z$ is unique only up to multiples of $2 k \pi$.

With this understanding, we can limit the choice of what $\theta$ can be for any given $z$ by requiring that $\theta$ lie in some half open interval of length $2 \pi$.

The most usual of these are:
 * $\hointr 0 {2 \pi}$
 * $\hointl {-\pi} \pi$

but in theory any such interval may be used.

This interval is known as the principal range.