CA Defs

Question 1

State the definition of a Möbius transformation.

Answer 1

A Möbius transformation is a mapping f : C ∪ {∞} → C ∪ {∞} of the form

f(z) = (az + b) / (cz + d)

in which a, b, c, d ∈ C, ad - bc != 0.

Question 2

State the definition of a fixpoint of a Möbius transformation.

Answer 2

A fixpoint of f is w ∈ C ∪ {∞} with f(w) = w.