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

• Dec 18th 2009, 04:03 PM
zzzhhh
which interval is commonly accepted for principal argument of complex numbers?
$\displaystyle (-\pi,\pi]$ or $\displaystyle [0,2\pi)$? since different definition may make the value of complex power different. Thanks!
• Dec 18th 2009, 05:35 PM
mr fantastic
Quote:

Originally Posted by zzzhhh
$\displaystyle (-\pi,\pi]$ or $\displaystyle [0,2\pi)$? 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
• Dec 18th 2009, 07:56 PM
zzzhhh
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.