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November 3rd, 2015, 02:43 PM  #1 
Newbie Joined: Nov 2015 From: UK Posts: 1 Thanks: 0  How do you show a Möbius transformation maps circles to circles and lines?
So I have been trying to prove this for a week now. It is driving me crazy So the general equation of a circle is : (xa)^2 + (yb)^2= r^2 and you put that in the form zz ̅ – (z+z ̅) α + (zz ̅ )αi = r^2 α^2 which in the wplane is 1/(ww ̅ )  ((w ̅+w)/(ww ̅ ))α + ( (w ̅w)/(ww ̅ )) αi = r^2 α^2 now if the centre α = o  how do you prove that it maps to a line? Last edited by skipjack; November 3rd, 2015 at 03:16 PM. 

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circles, hod, lines, maps, möbius, mobius, show, transformation 
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