The present work briefly develops the lectures which we have given since 1930 to the engineering candidates who chose the section of electromechanics at the Faculte polytechnique de Mons.

A memoir by Steinmetz 1 emphasized the simplifying role that can be played by the geometric interpretation of complex numbers in the study of the characteristic diagrams of electrical machines. This idea has proved fruitful in its developments, and many articles published in such journals as the Archiv fur Elektrotechnik can be comprehended only by the engineer acquainted with the meaning and the results of a plane analytic geometry adapted to representations in the Gauss plane. One there encounters, for example, unicursal bicircular quartics discussed by commencing with their parametric equation in complex coordinates; the procedure consisting of returning to classical geometry by the separation of the real and the imaginary will more often than not be devoid of interest, for it hides the clarity of certain interpretations which employ the relation between a complex number and the equivalent vectors capable of representing this number.

Geared toward readers unfamiliar with complex numbers, this text explains how to solve the kinds of problems that frequently arise in the applied sciences, especially electrical studies. To assure an easy and complete understanding, topics are developed from the beginning, with emphasis on constructions related to algebraic operations. 1956 edition.