I've been wondering how we take the logarithm of a periodic function. At least I think that's what I've been wondering - but I may have confused the terminology. Anyway, take, for example, the expression:
$\ln (-1)$
Well, $e^{i\pi} = -1$, so, by the definition of logarithms, $\ln (-1) = i\pi$. But $e^{3i\pi} = -1$ and so does $e^{5i\pi}$, etc., etc. So $\ln (-1)$ could also equal $3i\pi$.
So, is the logarithm function multivalued - are $i\pi$, $3i\pi$ and $5i\pi$ all valid answers - or do we take a kind of "principle value", or something else?
It's been a long time since I did logs and quite a long time since I did $e$, so my understanding of the basic principles may just be off.