O corpo dos números complexos sob a ótica histórica, prática e didática

Abstract

The study of Complex Numbers does not have much empathy of some math teachers. They claim that it is unnecessary and does not have many practical applications, or even worse, that they do not understand it well and, therefore, end up not including it in their classes. In order to contribute to changing this scenario, the purpose of this dissertation is to present the reader with a more in-depth approach to Complex Numbers, from the motivations for their appearance, formalizations, definitions, properties, applications (complex functions), to more sophisticated topics, such as: Complex Mappings, Möbius Transformations and the Circle-Preserving Theorem. It is important to note that, in contrast to certain traditional bibliographies used in undergraduate courses, this study follows a more didactic perspective; simplified and interactive, through mathematical softwares such as GeoGebra and Wolfram Alpha. This allows for a global view of Complex Numbers, makes their understanding more meaningful, no longer mechanical and tiresome, and may serve as a learning tool for high school and college students and teachers.