Explorando as propriedades geométricas no ensino dos números complexos

Abstract

This course conclusion work presents a Complex Numbers of teaching proposal exploring its geometric properties and the use of polar coordinates based on the trigonometric form of this set. The proposed activities are explored in detail the rotation operations, contraction and expansion in the plan, provided by the multiplication operations and leveraging Complex Numbers. It also displays up a meeting with the regular polygons by root extraction of complex numbers and explores the calculation of the area of these polygons leading to generalization of a formula to find the area of a regular polygon of n sides generated from nth root of a complex number. These proposals have the aim of expanding the forms of display and discussion of Complex Numbers and are directed to high school math teacher who seeks new teaching strategies.