Math Help - which interval is commonly accepted for principal argument of complex numbers?

1. which interval is commonly accepted for principal argument of complex numbers?

$(-\pi,\pi]$ or $[0,2\pi)$? since different definition may make the value of complex power different. Thanks!

2. Originally Posted by zzzhhh
$(-\pi,\pi]$ or $[0,2\pi)$? since different definition may make the value of complex power different. Thanks!
It is a matter of convention. See for example Arg (mathematics) - Wikipedia, the free encyclopedia

3. But what on earth is the convention commonly accepted in mathematical world? I have consulted wikipedia before posting this question, which directed me to this page saying both intervals are OK. This made me confused because, as I indicated in my post, different definition will lead to different complex power but ambiguity is not allowed in mathematics.