1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Mapping of Functions (Complex Analysis)

  1. Oct 3, 2012 #1
    1. The problem statement, all variables and given/known data

    Show that the function w = e^z maps the shaded rectangle in Fig X one-to-one onto the semi-annulus in Fig y.

    Fig x is the rectangle -1<x<1 ; 0<y<(x+pi(i))

    Fig y is the semi-annulus such that y>0 and -e<r<-1/e


    2. Relevant equations

    ....


    3. The attempt at a solution

    I'm not quite sure how to show the function is one-to-one. Any tips would be much appreciated.
     
  2. jcsd
  3. Oct 4, 2012 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    If e^z1=e^z2, then e^z1/e^z2=1=e^(z1-z2). 0<y<(x+pi(i)) looks a little odd if i is the imaginary unit. You don't write inequalities with complex numbers. What is 'i'?
     
    Last edited: Oct 4, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook