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, $[0,2\pi)$?