The Math Forum

Search All of the Math Forum:

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

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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 ]

Posts: 359
Registered: 9/16/06
Re: What's the geometry meaning of i^i ?
Posted: Jul 26, 2012 3:46 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Jul 25, 9:28 am, Hongyi Zhao <> wrote:
> Hi all,
> What's the geometry meaning of i^i ?  Here, i is the imaginary unit.
> Regards
> --
> .: Hongyi Zhao [ hongyi.zhao AT ] 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

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.



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

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.