I am confused. If you cam "do it perfectly on complex numbers" why can't you do it for this complex number?
Do you mean you can find the modulus and principle argument for something like a+ bi? I presume, then, that you know the modulus is and the "principle argument" is the principle value for the arctangent function, .
Then how could you have a problem here? With and you should be able to see immediately that because for all .
And surely you can do .
I think the difficulty is that this problem is too easy!