Some fundamental problems of science and engineering can be modeled by systems of nonlinear polynomial equations with complex coefficients, where the numerical solution plays an important role to solve them. This article shows some results of the numerical solution to such systems, commonly used in signal processing, filter design, equalizers, decouplers and other components of mobile phones, for instance. Some results are reported using the particle swarm algorithm, a modification and the traditional multidimensional Newton-Raphson. An advantage in terms of accuracy, computation time and number of iterations was observed for the modified algorithm.