Imaginary Numbers Raised to Imaginary NumbersDate: 12/29/2001 at 23:10:01 From: Dan Subject: Imaginary numbers raised to imaginary numbers Hello. I was fooling around with my TI-89 graphing calculator, and I input i^i, because of my infinite curiosity. The calculator returned e^(-pi/2). I went to your FAQ and read all I could about imaginary numbers and e, but it didn't really explain how or why i^i produced that. If you could explain, it would be a great help. Thanks a lot! Dan Date: 12/30/2001 at 04:51:59 From: Doctor Anthony Subject: Re: Imaginary numbers raised to imaginary numbers We can write i = [cos(pi/2) + i.sin(pi/2)] = e^(i.pi/2) and raising both sides to power i we get i^i = [e^(i.pi/2)]^i = e^(i^2.pi/2) = e^(-pi/2) = 1/e^(pi/2) = 0.2078795 - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/ |
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