When and why was the number plane invented and who invented it?

Question

Who why and when was the number plane invented

Answer 1

This is s long story, you may read it here:
http://www.clarku.edu/~djoyce/complex/

"By the end of the 18th century numbers of the form x + yi were in fairly common use by research mathematicians, and it became common to represent them as points in the plane. "

"This particular display of numbers of the form x + yi is attributed to various individuals including Wessel, Argand, and Gauss."
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Answer 2

probably the tax man.