The goal is to teach the fundamental and important concepts and techniques of complex analysis. It includes: 1- Providing the basic algebraic properties of complex numbers and fundamental concepts related to complex number sets, such as open sets, accumulation points, and boundary points; 2- Introducing the concepts of limit, continuity, and derivative, which are essential for studying functions of two complex variables; 3- Presenting the complex versions of elementary functions encountered in Real Analysis and examining their properties; 4- Introducing the integration of real-variable complex functions and complex functions in general (contour integration), demonstrating the fundamental properties of these integrals, and presenting the complex versions of the fundamental theorem of Calculus.

To understand complex variables and perform arithmetic operations. To classify and solve complex functions. To understand the basic solutions of complex equations. Introduction to the system of complex numbers; Limits, continuity, and derivatives of complex-valued functions; Cauchy-Riemann equations; Analytic functions; Harmonic functions.