And, as Euler's successor, Carl Friedrich Gauss, was to discover, if you plot real numbers on one axis of a graph and imaginary ones on the other, you create a plane that represents both sorts of numbers.

ECONOMIST: Beno?t Mandelbrot

For instance, currently each plane is flying within a very large, imaginary "safety sphere", to maintain safe distances between airborne aircraft.

BBC: Sowing the seeds of tomorrow's aircraft

Complex numbers, which have a real and an imaginary part added together, are the points on this plane that do not lie on either axis.

ECONOMIST: Beno?t Mandelbrot