# Definition:Argand Diagram/Historical Note

## Historical Note on Argand Diagram

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.

## Sources

- 1983: Ian Stewart and David Tall:
*Complex Analysis (The Hitchhiker's Guide to the Plane)*... (previous) ... (next): $0$ The origins of complex analysis, and a modern viewpoint: $1$. The origins of complex numbers - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $-1$ and $i$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $-1$ and $i$