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Originally Posted by Adam Y.
Yeah that though I was thinking more along the lines of hideous calculus that I have never taken yet. Aparently it has something to do with the taylor series. This is odd because I even asked my calculus teacher and he didn't know the reason why. He thought my friend was making it up
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Really? Euler's formula is pretty famous (well among engineers and mathematicians, anyway). It's some interesting stuff, if you look into it. Extending real functions to work with complex arguments is fascinating (and the basis for the formula). It works for the natural logarithm and a host of other functions (though not all the familiar properties always cary over). It comprises a field called analysis ... and if you want to talk about a really odd math problem, how about proving that all the non-trivial zeroes of the Riemann zeta function have real part equal to 1/2?
p.s. it might be a bit harder than the above trig "proof"
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My calculus teacher went through this proof a couple months ago. I'll try to see if I still have my pages of notes from that. But I remember it is from Talyor Series while using a polar system.
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The link above explains it ... or you can try
wikipedia's explanation (although it's funner to prove it yourself).