For the complex numbers question with finding n, I wrote n=6(2k-1), k is an element of Z, then said that this gave two unique solutions when k=0,1, the there would be two unique solutions when n=-6 and n=6. I then did the same as ZanyCat for the part after.
I thought that due to n being the power, the arg() could have been anything. The angle is usually restricted, but that would be converted in the final answer, not restricting the number of values for n. However, there were only two unique z1^n, where n satisfied the earlier condition. I think if you quoted any two for the second part, it would have been correct as long as they gave i and -i.
TL;DR: I agree with ZanyCat.