Definition:Argand Diagram

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An Argand diagram is a graphical representation of a set of complex numbers on the complex plane:


Also see

$\mathsf{Pr} \infty \mathsf{fWiki}$ makes the distinction between the diagram itself and the complex plane in which it is embedded.

Source of Name

This entry was named for Jean-Robert Argand.

Historical Note

The Argand diagram appears in Jean-Robert Argand's self-published $1806$ work Essai sur une manière de représenter les quantités imaginaires dans les constructions géométriques (Essay on a method of representing imaginary quantities by geometric constructions).

This would have passed unnoticed by the mathematical community except that Legendre received a copy.

He had no idea who had published it (as Argand had failed to include his name anywhere in it).

Legendre passed it to François Français.

His brother Jacques Français found it in his papers after his death in $1810$, and published it in $1813$ in the journal Annales de mathématiques pures et appliquées, announcing it as by an unknown mathematician.

He appealed for the author of the work to make himself known, which Argand did, submitting a slightly modified version for publication, again in Annales de mathématiques pures et appliquées.

By this time, however, Carl Friedrich Gauss had already himself invented the same concept.

It must be noted that this concept had in fact been invented by Caspar Wessel as early as $1787$, and been published in the paper Om directionens analytiske betegning by the Danish academy in $1799$.

This paper was rediscovered in $1895$ by Sophus Juel, and later that year Sophus Lie republished it.

Wessel's precedence is now universally recognised, but the term Argand diagram has stuck.