O movimento lógico-histórico dos números complexos integrando álgebra e geometria

Abstract

The focus of this study is to understand the logical-historical movement of complex numbers and their algebraic and geometric relationships, using the GeoGebra software to enhance the teaching-learning process of this content. It aims to establish conceptual connections between algebra, geometry, and the logical-historical trajectory of these numbers, considering the pedagogical interaction between technology and mathematical education. The objective is to contribute to the development of this topic, transcending traditional didactic strategies that often neglect the historical and geometric aspects. The research seeks to provide a more comprehensive and intuitive understanding of these numbers. The research is grounded in a historical-cultural perspective. This approach emphasizes the reconstruction of the scientific path of mathematical concepts. Using GeoGebra, we developed activities that illustrate operations and properties, providing a learning experience that integrates algebraic and geometric aspects. The investigation revealed the evolution of complex numbers, detailing the solution of cubic equations and the contributions of Scipione del Ferro, Tartaglia, Cardano, Bombelli, Euler, Wessel, Argand, Gauss, among others. The demonstrations of De Moivre's formulas and the nth roots are noteworthy for their importance and beauty. This research offers an integrated pedagogical approach in line with historical and technological processes, in harmony with the past and present, without losing sight of the future. The research shows potential to improve the teaching of scientific topics, benefiting not only the learning of complex numbers but also expanding pedagogical possibilities in other areas of mathematics. The study emphasizes the benefits of this methodology for teachers and students, suggesting paths for a richer and more meaningful academic education.