O Estudo da Reta no Plano Complexo

Abstract

This work aims to investigate the study of the straight line in the complex plane, highlighting how the concepts of Analytic Geometry, traditionally explored in the Cartesian plane, can be reinterpreted and applied to complex numbers, through an exploratory bibliographic research, developed from a qualitative perspective. First, a brief historical overview will be provided, followed by a consideration of the definition and elementary properties of complex numbers, emphasizing their algebraic and geometric representations, in order to develop the essential theoretical foundations for understanding the straight line in the complex plane. This analysis will examine its equations, properties, and mathematical implications, aiming to broaden the understanding of the relationships between Algebra and Geometry, without intending to exhibit or explore specific applications. It is also worth noting that the work prioritizes an algebraic approach, while still considering geometric interpretations when necessary.