Extensões do conceito de número com ênfase nos complexos e quatérnios

Abstract

The present dissertation aims to show the algebraic systematization of the sets N, Z, Q, R and C as extensions that preserve arithmetic and algebraic properties. Despite this fact, we will see that this field studies is not limited there. We will present that after C there is a formalization of Hamilton´s quaternions, also known as hypercomplex numbers. And these, like the other sets, are very important for mathematics and the environment we live in. Furthermore, we seek to approach the complex numbers in a dynamic that allows observe its importance in general. Therefore, this work intends to deepen the study on the subject in question leaving scope for the need for professional development. Making noticeable diversified forms to be developed in the teaching-learning process that enable a differentiated learning that will underpin the student knowledge for personal, social and academic future. In developing this dissertation, we started with the process of systematization of natural numbers to real. Consequently we commented on the emergence and formalization of complex numbers where then we exposed its usefulness in a global way. Lastly, we closed this work with an approach on Hamilton´s quaternions, traveling in a different mathematical field, important and encouraging us go deep in scientific research.