Números complexos e a transformação de Mobius

Detalhes bibliográficos
Ano de defesa: 2013
Autor(a) principal: Pereira, Helder Rodrigues
Orientador(a): Melo, Maurílio Márcio lattes
Banca de defesa: Melo, Maurílio Márcio, Santos, Walter Batista dos, Santos, Fabiano Fortunato Teixeira dos
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Federal de Goiás
Programa de Pós-Graduação: Programa de Pós-graduação em Matemática (IME)
Departamento: Instituto de Matemática e Estatística - IME (RG)
País: Brasil
Palavras-chave em Português:
Palavras-chave em Inglês:
Área do conhecimento CNPq:
Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tede/3094
Resumo: The set of complex numbers arose from the necessity of expanding the set of real numbers with the aim of solving algebraic equations. That has happened in Europe in the sixteenth century. Great Italian mathematicians as Scipione , Tartaglia, Cardano and Bombelli, contributed. This was the initial step that now allows us to know the square root of a negative number. A set numeric need not necessarily associated elements numbering, measuring or a count. O set of parts, a set of objects, provided the operations union and intersection, can be a set number even if its elements are not numbers. The body unordered of the complex numbers is a set of numbers (where the numbers are ordered pairs ) and can be represented by other structures, isomorphs to this set as the square matrices as two or classes of residual polynomial. Certain complex functions contribute for a better understanding of geometric transformations. The transformation of M obius is a good example of complex function,applied on a curve that can generate the e ects of rotation, translation, dilation (or contraction) and inversion.