Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Gottfried Helms

Posts: 1,903
Registered: 12/6/04
Re: What's the geometry meaning of i^i ?
Posted: Jul 26, 2012 8:18 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Am 26.07.2012 07:09 schrieb Hongyi Zhao:
> On Thu, 26 Jul 2012 05:21:56 +0200, Gottfried Helms wrote:
>

>> ... using rectangular coordinates and interpret them as polar ones (in
>> principle)?

>
> What do you mean, could you please give some more detail explanations?
>
> Regards
>

Hmm. Assume z0 = a + b*i where i is the imaginary unit.
Then consider
z1 = e^z0 = exp(z0) = e^a * e^(bi)
and e^a defines the length and e^(bi) the arc of the vectorial
representation of z1. Assume then new letters for the rectangular
coordinaters of z1:
z1 = A + B*i
Then consider the iteration
z2 = e^z1 = e^A * e^(Bi)
So the exponentiation can be understood as re-intrpretation
of the rectangular coordinates as coordinates in a polar representation.

Using i instead of e as basis for the exponentiation adds
a bit of complication, since i = e^(Pi/2*i), but that
complication is not so weird...


Gottfried



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.