Complex number paradox

  • #1
Nothing much, I have this:
gif.latex?\dpi{150}%20e^\theta=(e^{i\theta})^{-i}=(e^{i(\theta+2\pi)})^{-i}=e^{\theta+2\pi}.gif


I have studied (myself) about this for many days.
And I believe that, for some conditions
gif.latex?\dpi{150}%20(e^\psi)^\phi\neq%20e^{\psi\phi}.gif
for a complex ψ,ϕ

What are those conditions I mentioned about? And which field of study I should go to see?
 

Answers and Replies

  • #2
mathman
Science Advisor
8,046
535
Your first equation is obviously wrong, as you can see. For the second question, there are no conditions where it doesn't hold.

The problem lies in the fact that for non-integer exponents, the expression is not single valued.
 

Related Threads on Complex number paradox

  • Last Post
Replies
10
Views
4K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
8
Views
3K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
10K
  • Last Post
Replies
3
Views
794
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
10
Views
4K
Top