Mobius transformation

Hi, got a couple of mobius transformation qs:

a) Prove that every Mobius transformation for which infinity is a fixed point is of the form
z -> az+b

Can you just say that limit as z goes to infinity of a mobius transformation is a/c and thus for this to go to infinity we require c goes to 0, thus MT of the form (a*/d)z+(b*/d) = az+b?

b) Prove that the MT z-> az+b, with b not equal to 0, has 1 fixed point in extended complex plane for a=1 and 2 fixed point for a not equal 1

I have set z=az+b s.t. z=b/(1-a) but not sure how I can prove the number of fixed points!

Any help would be greatly appreciated!Thanks!

Reply 1

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