Complex Representation

The recognition that complex numbers admit a geometrical interpretation, as points in the Euclidean plane, was a critical step in securing their widespread acceptance (see §4.1). The “geometric algebra” of points in ℝ² defined by the arithmetic rules for complex numbers allows us to multiply and divide points, as well as adding or subtracting them in the usual vector sense. However, the systematic use of complex numbers as a means of exploring analytic geometry in ℝ² has received less attention than it deserves — The Advanced Geometry of Plane Curves and Their Applications¹ by C. Zwikker [480] seems to be the only treatise that consistently employs this approach.