Transformações de Möbius: uma proposta de ensino lúdico para alunos do ensino médio

Abstract

The work presented here aims to present an approach to the study of complex numbers, introducing the concept of Möbius Transformations for high school students, through playful activities. In it, presents the historical aspects of complex numbers, their algebraic structure and representation on the Cartesian plane, to later insert the study of functions involving complex numbers, in order to significantly complement the study of such content. The dissertation is justified by the fact that many students have difficulties with the algebraic manipulations of complex numbers, as well as the behavior of their operations on the Cartesian plane. Aiming at a qualitative character, the playful methodology was chosen as the primary tool to facilitate the studies of Möbius Transformations. We also use the foundations of some pedagogical theoreticians, historians and students of Mathematics, in order to relate the student's cognitive development, contributing to their social formation and, possibly, arousing interest in the discipline.