Explorando o tratamento matricial para uma introdução aos números complexos

• Ano de defesa: 2013
• Autor(a) principal: Gomes, Márcio Roberto
• Orientador(a): Pedroso, Kennedy Martins
• Banca de defesa: Ferreira, Ana Cristina , Entringer, Ariane Piovezan
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Viçosa
• Programa de Pós-Graduação: Mestrado Profissional em Matemática em Rede Nacional
• Departamento: Ensino de Matemática
• País: BR
• Palavras-chave em Português: Matrizes 2x2 especiais; Números Complexos; Ações geométricos de grupos
• Palavras-chave em Inglês: Matrices 2x2; Complex numbers
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://locus.ufv.br/handle/123456789/5883

The objective of this work is to give a more geometric approach in the introduction of complex numbers in order to make them more compreenssíveis and eliminating the idea of strange numbers and difficult to understand. To achieve this far will be a study of the properties of matrices 2x2 operative type [ a −b b a ] ,with a, b ϵR, reaching the result that these matrices form one body. Then associated with such matrices to points on the plane R2. From the result of this association gets to multiply a vector by a matrix of this type corresponds to a spin efeturar and multiply it by a scalar. From then makes two-way matching between the matrices and complex numbers so that all properties studied in the previous section remain true. As a result of this correspondence we obtain that multiplying by i2 corresponds to a spin 180o , I.e., keep the direction and reverse direction which corresponds to multiplying by (−1), I.e., i2 = −1 . Thus one arrives at a result which is usually presented to students in the introduction of complex numbers but with a meaning that once lacked. Then did a study of compliance and deformation of transformations of variables through functions complexas.Com this approach is facilitated understanding by students of their same concepts and the same function, to conclude we present a practical situation in which it uses the complexs numbers.