Why is the principal square root of a complex number defined as $\sqrt z = \sqrt r e^{-i \varphi / 2}$ for $\varphi \in (-\pi, \pi]$ ?
Wouldn't it be more natural to let $\varphi \in [0, 2\pi)$ as it is usual for polar coordinates?
If you think that you are free to choose whatever variant you like, then it's not quite the case. Software libraries definitely prefer the first one so if you are to take some assistance from a computer you are forced to use $\varphi \in (-\pi, \pi]$.