Argand diagram

Argand diagram

An Argand diagram, also known as the Argand plane or the complex plane, is a way of representing complex numbers as points on a coordinate plane using the x-axis as the real axis and the y-axis as the imaginary axis. It is named for the French amateur mathematician Jean Robert Argand (1768–1822) who described it in a paper in 1806.1 A similar method had been suggested 120 years earlier by John Wallis and had been developed extensively by Casper Wessel. But Wessel's paper was published in Danish and wasn't circulated in the languages more common to mathematics at that time. In fact, it wasn't until 1895 that his paper came to the attention of the mathematical community – long after the name "Argand diagram" had stuck.


In the diagram shown here, a complex number z is shown in terms of both Cartesian (x, y) and polar (r, θ) coordinates.



1. Argand, R. Essai sur une manière de représenter les quantités imaginaires dans les constructions géométriques. Paris: Albert Blanchard, 1971. Reprint of the 2nd ed., published by G. J. Hoel in 1874. First edition published Paris, 1806.