Análise Complexa: distinções entre o Corpo dos Números Complexos e o Corpo dos Números Reais

Abstract

This monograph presents a study based on complex numbers, presenting in a very detailed way the main concepts, definitions, properties, propositions and theorems related to this field. This study aims to build a narrative from a historical point of view, where the history of complex numbers allows us to visualize how and why this field came about. This research discussed the differentiability in the set of complex numbers, in contrast to the differentiability in the set of real numbers. The Fundamental Theorem of Algebra and the Cauchy-Riemann Equations are also presented in the text. In addition to the above objective, this research rigorously explains the essential differences between the two fields: complex numbers and real numbers. In the methodological approach, a qualitative bibliographic research was adopted.