Propostas para o ensino de números complexos no ensino médio

• Ano de defesa: 2014
• Autor(a) principal: Silva, Fabiana Gerusa Leindeker da
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• dARK ID: ark:/26339/0013000011c2v
• Idioma: por
• Instituição de defesa: Universidade Federal de Santa Maria; Brasil; Matemática; UFSM; Programa de Pós-Graduação em Matemática em Rede Nacional; Centro de Ciências Naturais e Exatas
• Palavras-chave em Português: Geometria; Números complexos; Forma polar; Rotações; Estratégias de ensino; Geometry; Complex number; Rotation; Polar form; Teaching strategies; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://repositorio.ufsm.br/handle/1/21530

This work explored the geometric properties of complex numbers. It presents a brief histor- ical contextualization, formalize the concepts, passing through the presentation of its algebraic form to its polar form and its geometric derivations. By means of this geometric bias is exam- ined in detail the operations of rotation, contraction and dilatation in the plane proportioned by the product of complex. As a consequence, we present an alternative proof of Napoleon’s Theo- rem, using immediately the product of complex numbers. Furthermore, are presented alternative proposals of work exploiting the interpretation of the analytic geometry problems experiencing efficient use of the properties of rotation resulting from the multiplication of complex num- bers. These proposals are directed to mathematics teachers in the 3rd year of high school with the goal of expanding the forms from presentation and treatment of complex numbers in their strategies for teaching this topic.