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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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Narasimham

Posts: 116
Registered: 9/16/06
Re: What's the geometry meaning of i^i ?
Posted: Jul 26, 2012 3:46 AM
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On Jul 25, 9:28 am, Hongyi Zhao <hongyi.z...@gmail.com> wrote:
> Hi all,
>
> What's the geometry meaning of i^i ?  Here, i is the imaginary unit.
>
> Regards
> --
> .: Hongyi Zhao [ hongyi.zhao AT gmail.com ] Free as in Freedom :.

i^i is not an imaginary number or numbers, but a set of equally spaced
real numbers.

Just as product of two negative numbers returns
positive,exponentiation of pure imaginary numbers returns as pure real
number.

From Euler's identity the set is seen to be odd multiples of pi/2,
(4*k + 1)pi/2. Geometrically seen on the Argand diagram they are all
on the real axis, say formed by a point of a rolling circle 2 units
radius rolling on real axis. i.e., (.., -7,-3,1,5,9, ..)* pi/2.

HTH

Narasimham

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