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Homework Help: 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


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    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
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