Complex variables is both a very general topic that permeates numerous areas of mathematics, such as linear algebra, trigonometry, and calculus, as well as a very specialized method for solving partial differential equations, conformal mapping, and evaluating real definite integrals. The following videos cover basic arithmetic, algebra, trigonometry, and calculus involving complex numbers, variables, and functions as well as conformal mapping and solving Laplace's equation using complex variable methods. They are based on these lecture notes.
YouTube Videos: Chapter 1 - Functions of a Complex Variable
YouTube Videos: Chapter 2 - Conformal Mapping and Boundary-Value Problems
YouTube Videos: Chapter 3 - Integration in the Complex Plane