This representation is known as an Argand diagram.
Also known as
Some sources refer to this as an Argand plane.
It is also sometimes known as a Gauss Plane, or Gaussian Plane, but as it is now recognised that neither Gauss nor Argand had precedence over the concept of plotting complex numbers on a plane, the more neutral term complex plane is usually preferred nowadays.
Source of Name
This entry was named for Jean-Robert Argand.
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).
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.
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 $1799$.
Wessel's precedence is now universally recognised, but the term Argand Diagram has stuck.
- 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 2$. Geometrical Representations
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $6$: Graph of a Complex Number
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Graphical Representation of Complex Numbers
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Entry: Argand diagram (complex plane)
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: Argand diagram