3.I.2D

Show that the set of Möbius transformations of the extended complex plane $\mathbb{C} \cup\{\infty\}$ form a group. Show further that an arbitrary Möbius transformation can be expressed as the composition of maps of the form

$f(z)=z+a, \quad g(z)=k z \text { and } h(z)=1 / z$

*Typos? Please submit corrections to this page on GitHub.*