Argand, Jean Robert (1768–1822)

A complex number can be represented graphically as a line whose end-point coordinates equal the real and imaginary parts of the complex number. This type of diagram is called an Argand diagram after the French mathematician Jean Argand (1768–1822) who devised it.

Swiss mathematician. In 1806 he invented a method of geometrically representing complex numbers and their operations – the Argand diagram.

Argand was born in Geneva and later moved to Paris. He appears to have been entirely self-taught as a mathematician.

Argand adopted Descartes's practice of calling all multiples of √−1 ‘imaginary’. He demonstrated that real and imaginary parts of a complex number could be represented as rectangular coordinates.

The diagram is a graphic representation of complex numbers of the form a + bi, in which a and b are real numbers and i is √(−1). One axis represents the pure imaginary numbers (those belonging to the bi category) and the other the real numbers (those belonging to the a category); it is thus possible to plot a complex number as a set of coordinates in the field defined by the two axes.

Argand's book Essai sur une manière de représenter les quantités imaginaires dans les constructions géométriques (1806) was published anonymously and it was not until 1813 that he became known as the author.