Complex numbers and vector electrical magnitudes under the optics of the Theory of the Registers of Semiotic Representations

Abstract

This article discusses how the mathematical concept of complex number is introduced in some textbooks used in electrical circuits, as regards the presence of semiotic representations of the complex numbers and the semiotic representations the electrical related quantities. The theoretical basis was given by the theory of Semiotic Representations records for Raymond Duval and the methodological procedures sought to follow the content Analysis methodology of Laurence Bardin. Set out the categories of analysis, we sought to investigate qualitatively and quantitatively the presence of semiotic representations of complex numbers and electrical quantities in four textbooks, and cognitive transformations of these representations. It was concluded that, in these books, the algebraic representations and algebraic polar Cartesian predominate in the approaches of complex numbers and, consequently, also the conversions of these types of representations. This article shows the applicability of the theory of Semiotic Representations records in related fields of mathematics.