So, here's what I'm having trouble with:
so for e^x+1=0, I knew that if I let e^x = 1 and e^(iy) or (cosy+ isiny) = 2(pi)n, I can have solutions. But how do I know that is the only solutions? That is, how do I know that there aren't some e^x(cosy) =1 that aren't listed by above method? For example, some e^x bigger than 1 and some cosy smaller than 1 and somehow make up the number 1? ... Oh wait... I think I just answered my own question.