Methodological proposal for the solution of polynomial equations in the field of complex numbers

Abstract

On many occasions in solving different technical problems we find ourselves with the task of solving polynomial equations of degree n, in which we need to find their roots, where within the probabilities we can have real or complex roots depending on the characteristics of the polynomial in question, the first that are widely used because there is a notion of these values and are very applicable in real problems, the second the complex roots that exist, these do not have a real notion, which sometimes are not considered in the solution of real problems, but on many occasions if it is necessary to consider them, as is the case of the solution of differential equations, among other applications, this implies that these roots must be found. For this reason, this study proposes a methodology for calculating the roots of polynomial equations of degree n, which involves a combination of different numerical methods and the respective conceptualization to find both real and complex roots, as intermediate information for the subsequent troubleshooting.