I would normally define e^z = sum_{n=0}^{infinity} z^n/n!. Then e^(pi i) = -1 is a non-trivial result. Some nominees for my favorite theorem: * The order of the element divides the order of the group. * Unique factorization of integers. * The intermediate value theorem. As you can see, I tend to favor simple but fundamental theorems. e^(pi i) = -1 is neat, but doesn't lead to anything. Franklin T. Adams-Watters -----Original Message----- From: Emeric Deutsch deutsch@duke.poly.edu On Fri, 28 Apr 2006, Steve Gray wrote:
... On these scores, e^(i pi)+1=0 is unbeatable.
I am sure that I am missing here something. What is the definition of e^(x+iy) ? Isn't it e^(x+iy)=e^x (cos y + i sin y) ? Emeric _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun ___________________________________________________ Try the New Netscape Mail Today! Virtually Spam-Free | More Storage | Import Your Contact List http://mail.netscape.com