"The first attempt (which was unsuccessful) to represent
complex numbers geometrically was made in the seventeenth
century by John Wallis. [1]
Where Wallis failed, a Norwegian surveyor succeeded; in 1799
Caspar Wessel (1745-1818) published the first explanation
of the geometrical representation of complex numbers. [2]"
[1] "The important passage from Wallis may be found in _A Source Book in
Mathematics_, ed. David Eugene Smith, vol. I, (New York, 1959), 46-54."
[2] "The words 'to publish' qualify this statement sufficiently that no
mention need be made in the text of Leonard Euler, Charles Walmesley, and
Dominique Truel. The basis for attributing the geometrical representation
to the first two of these men is that it seems from reading their writings
on relevant subjects that they probably had this representation. The sole
basis for mentioning Truel is a statement by Cauchy that Truel had this
representation as early as 1786. For a fuller discussion see Florian
Cajori, 'Historical Notes on the Graphic Representation of Imaginaries
before Wessel' in _American Mathematical Monthly_, 19 (1912), 167-171."
--JGC