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

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

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Ken S. Tucker

Posts: 5
Registered: 3/22/12
Re: What's the geometry meaning of i^i ?
Posted: Jul 27, 2012 1:22 AM
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Richard Tobin wrote:
> In article <junsli$7n8$1@aspen.stu.neva.ru>,
> Hongyi Zhao <hongyi.zhao@gmail.com> wrote:
>
>> What's the geometry meaning of i^i ? Here, i is the imaginary unit.
>
> We can naturally define b^x as e^(x log b). The principal value of
> log i is pi/2 i, so i^i is e^(-pi/2).
>
> All you need now is a geometric interpretation of log i. For an
> imaginary number the log is i times the phase, but I'm not sure
> that is really an interpretation.
> -- Richard

Unit length is one solution. (i^i)^4 =1 , 1^(1/4)=1.
Ken

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