Two things: 1. I said earlier that I already know how to find the numbers mathematically. What I don't have any intuition for is why the numbers are correct (s

Two things: 1. I said earlier that I already know how to find the numbers mathematically. What I don't have any intuition for is why the numbers are correct (such as why both e and pi should be in the answer). 2. You can't just distribute the exponents without justifying that it's valid. (I don't know the appropriate conditions for doing this myself either, but I know they exist.) For example (e^(2 i pi))^(1/2) is not e^(i pi), it's e^0. In other words, you need to first reduce it mod 2pi. Now if you're dealing with complex numbers I have no idea what the conditions should be.