Solution (source code)

= Solution

The assertion is \b[true]. A <Möbius map> fixes infinity if and only if $c=0$: if $c\ne0$, its value there is the finite number $a/c$. For $c=0$, the decomposition above uses only a nonzero complex scaling and a translation. These maps form the <Affine subgroup of the Möbius group>.