<Complex conjugation> fixes $0,1,\infty$, but sends $i$ to $-i$, so it is not the identity. The preceding classification of <fixed points of a Möbius transformation> says that a nonidentity <Möbius transformation> has at most two <fixed points>. Since <complex conjugation> has at least three, \b[it cannot be a <Möbius transformation>].

Solution

Past exam of the mathematics course of the University of Cambridge / 2002 / ia / Paper 1 / 6B / b / Solution

 Solution (source code)