V. Theory of the Imaginary

Abstract

As you know, the theory of imaginary quantities was first developed in algebra and analysis, especially in the theory of equations and in the theory of functions of a complex variable, where, indeed, it has celebrated its greatest triumph. In addition to this, however, at an early date, mathematicians had assigned to the variables x and y in analytic geometry complex values x = x ₁ + ix ₂, y = y ₁ + iy ₂, and had thus added to the real points a large manifold of complex points without, at first, assigning any proper geometric meaning to this manner of speaking, which had been borrowed from analysis.