The concept had appeared in print earlier, such as in work by Gerolamo Cardano. The imaginary numbers are on the vertical coordinate axis.ДЄlthough the Greek mathematician and engineer Hero of Alexandria is noted as the first to present a calculation involving the square root of a negative number, it was Rafael Bombelli who first set down the rules for multiplication of complex numbers in 1572.

Originally coined in the 17th century by RenГ© Descartes as a derogatory term and regarded as fictitious or useless, the concept gained wide acceptance following the work of Leonhard Euler (in the 18th century) and Augustin-Louis Cauchy and Carl Friedrich Gauss (in the early 19th century).ДЄn imaginary number bi can be added to a real number a to form a complex number of the form a + bi, where the real numbers a and b are called, respectively, the real part and the imaginary part of the complex number. By definition, zero is considered to be both real and imaginary. For example, 5 i is an imaginary number, and its square is в€’25. The square of an imaginary number bi is в€’ b 2. For the 2013 EP by The Maine, see Imaginary Numbers (EP).ДЄn imaginary number is a real number multiplied by the imaginary unit i, which is defined by its property i 2 = в€’1.

Imaginary numbers