Hyperbolic Geometry Watch

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Report Thread starter 7 years ago
I am having a bit of a problem with the question below. I have done question (i) and found the answer to be 3+2i. I am having a very hard time trying to understand what is required of question (ii). Any help would be greatly appreciated.

Define a Mobius transformation, M, of the hyperbolic upper half plane by
M(z) = (5z-13)/(z-1)

(i) Find the unique fixed point, P, of M in the hyperbolic plane and show that it lies on the h-line
'n' given by mod(z-6)=sqrt13
(ii) Determine the image, M(n), of the h-line n.
(iii) Find the angle at P between the positive ray n+ and its image, M^(n+). (Positive
here means emanating from P in the direction of increasing real part, x.)

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