# Why is principle value of argument generally taken as $(-\pi , \pi]$?

I have just started reading about the Modulus and Argument of Complex Numbers. In the definition, it is said that:

If z is not equal to 0 and $-\pi < \theta \le \pi$ , then $\theta$ is the principal argument of z, written $\theta = \arg(z)$.

My question is about the interval: why do we take $-\pi < \theta \le \pi$, which, if I understand it correctly starts at $180$ degrees, namely $-\pi$ (the most left point on the $x$ axis of the zero circle), and moves counter clockwise until it reaches $180$ degrees again? Why don't we use, say, $[0,2\pi)$?

• – Shaun Sep 3 '17 at 12:05
• Not much of an advantage, but in this principal value range, if $\arg(z) = t$ then $\arg(z^*)$ is $-t$. – samjoe Sep 3 '17 at 12:08