Introdução às Transformações de Möbius: aspectos geométricos e algébricos.

Abstract

Möbius transformations are important complex rational functions for mathematics and other areas. They belong to the set of maps that preserve angles, called conformal, and that are applied in various physical problems. The aim of this work is to introduce in a geometric and algebraic way the Möbius transformations, using basic geometry and encouraging its study through its application. For this, we will introduct preliminary notions of complex numbers, plane transformations, stereographic projection, Riemann sphere and the relationships between these concepts and Möbius transformations. Finally, we obtain algebraic classification for these transformations.