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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 25, 2012 1:15 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply wrote:
> On Wed, 25 Jul 2012 04:28:34 +0000 (UTC), Hongyi Zhao
> <> 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
Adorning every public street
And seem to breathe in stone, or
Move their marble feet.

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