Introduction to Theory of Complex Variables

Chapter 1 serves as a foundational introduction to the theory of complex variables, setting the stage for their application in econometrics. It begins with a historical overview of complex numbers, elucidating their development and conceptual underpinnings. The chapter then progresses to define and explain the properties of complex numbers, complex random variables, and the construction of complex-valued models. By discussing the theoretical aspects of complex variables, including their statistical implications, the chapter prepares readers to understand and leverage complex-valued approaches in econometric modelling. This groundwork is essential for the exploration of complex linear regression and correlation analysis in subsequent chapters.