This research is the result of the investigation on the Fundamental Theorem of
Algebra, of a quantitative methodological character, the procedures used during the research will be based on studies and analysis of books, articles and theses, we will elucidate in a sequential way the topics of the theme, with the objective of to analyze and investigate the historical development of complex numbers since the emergence of the square roots of negative numbers, with emphasis on the works of Scipione del Ferro, Girolamo Cardano, Rafael Bombelli and Carl Friedrich Gaus, focusing on the construction of the body of the set of complex numbers as an extension of the set of reals, and the definitions and properties of polynomials, in which they offer a structure for the consolidation of the Fundamental Theorem of Algebra. In this work we bring a fully algebraic proof, confirming the result that every non-constant polynomial, of degree, with complex coefficients, has at least one complex root. The research sought to bring an accessible and objective demonstration
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