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

• Ano de defesa: 2021
• Autor(a) principal: Sousa, Antônio Marcos Carvalho de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Lavras; Programa de Pós-Graduação em Matemática em Rede Nacional; UFLA; brasil; Departamento de Ciências Exatas
• Palavras-chave em Português: Números complexos; Transformações de Möbius; Teorema do círculo preservado; Aprendizagem significativa; Sequência didática; Complex numbers; Möbius transformations; Circle-preserving theorem; Meaningful learning; Didactic sequence; Matemática
• Link de acesso: http://repositorio.ufla.br/jspui/handle/1/46156

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.