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Math Forum » Discussions » sci.math.* » sci.math

Topic: What's the geometry meaning of i^i ?
Replies: 16   Last Post: Jul 29, 2012 2:34 PM

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Frederick Williams

Posts: 2,164
Registered: 10/4/10
Re: What's the geometry meaning of i^i ?
Posted: Jul 27, 2012 11:40 AM
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"Ken S. Tucker" wrote:
>
> Butch Malahide wrote:
> > On Jul 27, 12:22 am, "Ken S. Tucker" <dynam...@rocketmail.com> wrote:
> >> Unit length is one solution. (i^i)^4 =1 , 1^(1/4)=1.
> >
> > What did you mean by "(i^i)^4 =1"? Must be a typo, but a typo for
> > what??
>
> If memory serves,
> (i^i)^2 = i^2i= (-1)^i , (-1)^2i = 1^i = 1 = (i^i)^4 .
>
> I assume 1^(anything) = 1.
>
> Now 1^(1/4) = i^i = 1.
>
> Hows that?

It's wrong, that's how it is! The principal value of i^i is about 0.2.
Generally,

i^i = e^{-pi(2n + 1/2)}.

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