Complex Analysis focuses on the study of functions of complex variables, exploring their properties like differentiability and analyticity. It uses tools such as contour integrals, residues, and the Cauchy-Riemann equations for solving integrals and studying singularities. Numerical Methods, on the other hand, provide approximations to mathematical problems that cannot be solved exactly, including techniques for solving equations and differential equations. Common methods include Newton’s method, finite difference methods, and the Runge-Kutta method. Both fields are vital in applications like engineering, physics, and computer simulations.