Conformal Mapping: Sketch Regions & Find Mapping

  • #1
diorific
19
0
Hi, I need to sketche ach of the following regions: R = {z :|z| < √2, 7π/16 < Argz<9π/16}, R1 = {z :|z| < 16, Rez>0} and write down a one-one conformal mapping f1 from R onto R1.

Here is my sketch https://onedrive.live.com/redir?resid=4cdf33ffa97631ef%2110238

But I'm finding hard to find the mapping. So if someone can help me out that'd be appreciated.
 
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  • #2
As a start, I'd consider the mappings ##z \to z^\alpha## for various powers ##\alpha## and see what effect they have on ##R##.
 
  • #3
Ok thank you I think it's z→z^8
 
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