The Computation of Particular Roots of Nonlinear Complex Equations of the Form: 

Adel Al-Odhari^1,*, Shaker AL -Assadi²

¹Faculty of Education, Humanities and Applied Sciences (khawlan), and Faculty of Engineering, Sana'a University, Yemen

²Faculty of Sciences, Sana' University, Yemen

Emails: a.aleidhri@su.edu.ye; shakeralassadi@gmail.com

Abstract

Solving polynomial equations involves finding their roots. In this respect, this idea dominates the minds of many mathematicians about how to find those roots. The Abel–Ruffini theorem emphasizes that there is no general formula involving only the coefficients of a polynomial equation of degree five or higher that allows us to compute its solutions using radicals and its associate to the Galois Theory. The mathematical need for solving polynomial equations represents the motivation for the development of systems of numbers from Natural numbers to Complex numbers throughout the history of mathematics. Complex numbers play a central role in this context. The Fundamental Theorem of Algebra tell us that every nonconstant polynomial equation with complex coefficients has at least one complex root. While the Galois group associated with a polynomial captivates its symmetries and determines whether it is solvable by radicals. From a mathematical standpoint, it is customary to visualize polynomials in the form:

 Where the set of coefficients {    and  we have reconceptualized the polynomial generated by the formula   in our previous work and computing radicals of more degree 5. In this article, we present a natural procedure formula that will lead us to find a solution for a class of polynomials nonlinear Complex numbers with degree 𝑛 associated with the equation:     as a particular class of Complex Polynomials.

Keywords: Binomial Theorem; Complex Polynomials; Exact solving of non-liner Polynomials of Complex Numbers in particular class