A History of Complex Numbers

The first instance of a problem leading to an imaginary number is in Stereometrica by Heron of Alexandria from about AD 50. He was attempting to solve the expression [sq(81-144)]. In India around 850 Mahavira wrote "As in the nature of things, a negative is not a square, it has no square root." In 1545 Girolamo Cardano called complex numbers "fictitious". He did however work on the problem "Divide 10 into two parts such that the product ... is 40". Cardano found the solutions 5+sq(-15) and 5-sq(-15), but he said that to work these numbers would be "as subtle as it would be useless". Caspar Wessel came up with a graphical representation of complex numbers, however it was published in 1799 in a jounrel infrequently read by mathematicians. 100 years later he finally recieved the credit he deserved for work that would have greatly influenced the world of math.

The development of complex numbers was also aided by Rene Descartes who invented the terms "real" and "imaginary". In 1702 Gottfried Wilhem von Leibniz described complex numbers as "that wonderful creature of an ideal work, almost an amphibian between things that are and thing that are not". Leonard Euler introduced the letter i into the world of complex numbers.

It took the influence of Gauss for complex numbers to be universally accepted. Independently of Wessel, he plotted complex numbers on a plane.