Overview

Complex numbers are those numbers containing a term that is the square root of negative one. Initially viewed as impossible to solve, complex numbers were eventually shown to have deep significance and profound importance to our understanding of physics, particularly those parts of physics involving electricity and magnetism. Complex numbers were finally recognized as a legitimate branch of mathematics in the last years of the eighteenth century, and they have been regarded as indispensable to some fields since the early nineteenth century.

Background

In 1850 B.C. an unknown Egyptian mathematician wrote on a papyrus the formula for calculating the volume of a truncated cone, called a frustum [V = ¹/₃*H*(a² + ab + b²)]. Interestingly, the formula is identical to the one used today, although deriving and solving this formula is usually thought to require...