## Abstract

It is an obvious fact that the set of reals is too small to provide a complete description of the set of roots of polynomial functions; for instance, the function *x*↦*x*^{2} + 1, with \(x\in \mathbb R\), does not have any real root. Historically, the search for such roots strongly motivated the birth of complex numbers and the flowering of complex function theory. In this respect, a major first crowning was the proof, by Gauss, of the famous *Fundamental Theorem of Algebra*, which asserts that every polynomial function with complex coefficients has a complex root.

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