A Way to Express i to the i
Date: 17 Apr 1995 22:42:49 -0400 From: Denise L. Kunz 813 757-9370 Subject: Curious Dr. Math, I know e to the iA = cosA + i sinA, where iA is the exponent. Is there another way to express i to the i? Thank you. Denise Kunz (email@example.com)
Date: 18 Apr 1995 13:25:24 -0400 From: Dr. Ken Subject: Re: Curious Hello there! Stuff like this is really neat. One standard trick in evaluating weird powers is to make everything be a power with base e. So we can do that by writing i^i (which means i to the i) = e^Log[i^i] = e^(i*Log[i]). Then we use the fact that Log[i] = i*Pi/2 to get i^i = e^(i*i*Pi/2) = e^(-Pi/2). You can then use a calculator or the Taylor expansion for e^x to see that e^(-Pi/2) is about 0.20788. Nice question!! -Ken "Dr." Math
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