i (The Imaginary Unit)

Defined as a square root of negative one, a number no real number can be, since the square of any real number is never negative. Italian mathematician Rafael Bombelli worked with such quantities as a formal bookkeeping device as early as 1572, and Rene Descartes coined the very term imaginary in 1637, using it dismissively, to describe a quantity he regarded as fictitious and only useful for calculation. Leonhard Euler introduced the letter i for the quantity in 1777, and Carl Friedrich Gauss's later work helped establish the complex numbers, ordinary pairs of a real part and an i-multiplied part, as a fully legitimate and geometrically meaningful number system rather than a mere calculating fiction.