Description 
The field of complex numbers is an extension of the field of real numbers. Complex numbers and the function of complex variables have application in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, and particularly quantum mechanics.
In this course, we will study complex numbers, arithmetic of complex numbers, function of complex variables, limit, continuity, differentiation, integration of functions of complex variables and some important theorems on differentiation and integration, convergence of series, types of series, residues, poles, conformal mappings, and finally their applications.
