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!

Mobius Transformations

  1. May 9, 2007 #1

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    1. The problem statement, all variables and given/known data
    Find a Mobius transformation that maps the real axis to the circle |z-1|=1, and the line Im(z)=1 to the circle |z-2|=1


    2. Relevant equations
    A mobius transformation is one of the form [tex]z\rightarrow\frac{az+b}{cz+d}[/tex] on the extended complex plane

    3. The attempt at a solution

    My attempt pretty much comes out to... well, mobius transformations are bijections, but the two lines I'm given in the pre-image only intersect at infinity. So how do I get the two intersection for the circles? I'm thinking maybe I'm really dumb, and they're just tangent, but it looks to me as if they meet at [tex]\frac{3}{2}\pm\frac{\sqrt{3}}{2}i[/tex]
     
  2. jcsd
  3. May 9, 2007 #2

    AKG

    User Avatar
    Science Advisor
    Homework Helper

    You're right, there does seem to be a problem with the question.
     
  4. May 9, 2007 #3

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I asked someone about it, and it's actually |z|=1 and |z-2|=1, so they're tangent at a point (I was reading off the circle descriptions from the question above previously... whoops).

    I was having enough trouble with these stupid things without making them even more difficult for myself.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Mobius Transformations
  1. Mobius Transformation (Replies: 3)

  2. Mobius Transformations (Replies: 2)

Loading...