The "standard" argument for complex numbers lies between 0 and while "arctan" always gives a value between and . In the case of we are looking at which is ih the first quadrant so we add to get .

However, the "argument" of a complex number is not "uniquely" defined. Adding or subtracting to the argument will give another that is also a valid argument for that same complex number. Subtracting from , of course, gives the same as subtracting from . As I said before the "standard" is between 0 and but there might be good reason to use another representation.