In 1867, Jules Hoüel praised the efforts (‘ont rendu un immense service à la philosophie mathématique’) spent in the previous century to develop the algebraic operations and a graphical representation system for complex numbers, reviewed here in chapter 4. This corpus of notions was now ready to move on to the next stage and evolve definitely into the field of complex analysis, dedicated to exploring the behavior of functions in one or several complex variables [285, 1st part, p. 1].