Harmonic Solutions to Solve Complex Algebraic Equations

Abstract

Complex algebraic equations are a fundamental topic in mathematics, requiring the use of multiple techniques to solve them. These technologies include Simplifying, multiplying by reciprocals, and many other different methods, which is used to analyze equations and extract the required variables. Through this study, which aims to enhance students’ understanding of the basic concepts in algebra, including algebraic operations such as addition, subtraction, multiplication, and division, and how to apply them in solving equations, in addition to developing students’ level in solving complex algebraic equations using...? Combinatorial solutions and developing exploration and criticism skills through analyzing mathematical problems. Through a methodology that relied on several different methodologies, including the descriptive methodology in describing and defining complex algebraic equations and combinatorial solutions, and the quantitative methodology in collecting data on combinatorial solutions and the factors influencing the solution of complex algebraic equations and the nature of the compromise solutions that are chosen, in addition to the scientific methodology in analyzing combinatorial methods and the influencing factors. There is a comparison methodology to compare combinatorial methods in terms of accuracy, ease, and pass ability The results indicated that combinatorial solutions are largely effective in enhancing students' understanding of basic concepts and developing their skills. Exploratory and critical mathematical problems. The flexibility, ease and accuracy of combinatorial methods range from 90 to 95%.