The Geometry of Complex Numbers

Abstract

One can view the development of numbers as generated by the need to find solutions to more and more complicated equations. So the definition and use of negative integers was motivated by equations such asx + 1 =0, rational numbers by equations such as 2x — 1 = 0 and so on. Complex numbers were needed to find a solution to x²+ 1 = 0, that is $\sqrt { - 1}$. Each such advance in the use of numbers met some resistance from the current mathematical community. The use of complex numbers was no exception. Even the first user, Cardano in about 1539, who needed them to make sense of the solution of cubic equations was reluctant.

As far as I know, Car'dano was the first to introduce complex numbers $\sqrt { - b}$ into algebra, but he had serious misgivings about it