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

 Messages: [ Previous | Next ]
 Frederick Williams Posts: 2,164 Registered: 10/4/10
Re: What's the geometry meaning of i^i ?
Posted: Jul 25, 2012 1:15 PM

Pfsszxt@aol.com wrote:
>
> On Wed, 25 Jul 2012 04:28:34 +0000 (UTC), Hongyi Zhao
> <hongyi.zhao@gmail.com> wrote:
>

> >Hi all,
> >
> >What's the geometry meaning of i^i ? Here, i is the imaginary unit.
> >
> >Regards

>
> What on earth do you mean by "geometry meaning".

It's not for me to explain what the OP meant, but multiplication by i
corresponds to rotation about the origin by a quarter circle. That is
clearly geometrical; so it is reasonable to wonder what (if anything) is
the geometrical meaning of exponentiation.

> "i" is simply the point (0,1) in the plane!

And the principal value of i^i is about one fifth!!

--
The animated figures stand
And seem to breathe in stone, or
Move their marble feet.

Date Subject Author
7/25/12 Hongyi Zhao
7/25/12 Pfsszxt@aol.com
7/25/12 Frederick Williams
7/25/12 Brian Q. Hutchings
7/25/12 Gottfried Helms
7/26/12 Hongyi Zhao
7/26/12 Gottfried Helms
7/26/12 Narasimham
7/27/12 Narasimham
7/26/12 Richard Tobin
7/27/12 Ken S. Tucker
7/27/12 Butch Malahide
7/27/12 Ken S. Tucker
7/27/12 Frederick Williams
7/27/12 Ki Song
7/29/12 Michael Press
7/29/12 Brian Q. Hutchings