Mapping of Functions (Complex Analysis)

  • #1

Homework Statement



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


Homework Equations



....


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.
 

Answers and Replies

  • #2
Dick
Science Advisor
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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'?
 
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