Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Complex number paradox

  1. Oct 25, 2011 #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?
     
  2. jcsd
  3. Oct 25, 2011 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Complex number paradox
  1. Complex numbers (Replies: 15)

  2. Complex number (Replies: 6)

  3. Complex numbers? (Replies: 6)

  4. Complex numbers (Replies: 2)

  5. Complex numbers (Replies: 2)

Loading...