Propostas para o ensino de números complexos no ensino médio

Abstract

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.