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Sat 20 Aug, 2005 01:07 am
Hi all! I was wondering if anyone can provide me with an elegant proof for i to the i being real, where, i is the complex number sq. root of -1. All your input/help will be greatly appreciated. Thanks!
if e^(i*pi)=-1 is true
then i=e^(i*pi/2) is true
so i^i=[e^(i*pi/2)]^i
taking log, then
ln(i^i)=iln(i)=iln[e^(i*pi/2)]=i*(i*pi/2)=-pi/2
and i^i=e^(-pi/2)
Rap
Thanks!
Thanks a bunch guys!
That was actually a competition problem on a university site I ran across a little while ago. I don't remember where that was though.
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