Wow. You all must have posted right after I did.
First of all, to robly: The URL isn't working because you placed the [/url] before the ^i, which makes it search for (-1) and not (-1)^i. Also, like I said, there could be multiple answers to this. Giving one answer doesn't necessarily disprove the other answers.
Now to A Random Player/ARP: Yes, (-1)^i = e^(-pi). You can also find this through Euler's identity. In fact, I was thinking about posting that in the post before my previous post. Basically, because e^(i*tau/2)=-1, and e^(i*tau/2)^i=(-1)^i, which equals e^(i*i*tau/2)=(-1)^i, meaning e^(-tau/2)=(-1)^i. Even so, like I said, something can have multiple answers when you're working in the strange realm of powers and complex numbers, especially when you're working in both realms. (-1)^i may even be indeterminate. Any full counter-proofs yet?
Also, has anyone found the answer to the puzzle so far? sqrt(-1) think there might be a pattern with what I was doing. (
viewtopic.php?f=1&t=106#p700)
Nobody ever notices my signature. ):