# Imaginary numbers

If you take i and square it, you get a -1. Let’s go over that again: i*i = -1. As that’s not possible, it’s imaginary, which is why it’s represented by the letter i. However, in electrical engineering, "i" represents current, so we use the letter "j". In a graph, we represent the real numbers on the x-axis and the imaginary numbers on the y-axis, and when calculating impedance, imaginary numbers are a great way to show the varying resistance at different frequencies.

An **imaginary number** is a complex number that can be written as a real number multiplied by the imaginary unit *i*,^{[note 1]} which is defined by its property *i*^{2} = −1.^{[1]} The square of an imaginary number *bi* is −*b*^{2}. For example, 5*i* is an imaginary number, and its square is −25. Zero is considered to be both real and imaginary.^{[2]}

Originally coined in the 17th century by René Descartes^{[3]} as a derogatory term and regarded as fictitious or useless, the concept gained wide acceptance following the work of Augustin-Louis Cauchy, Leonhard Euler and Carl Friedrich Gauss.

An 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.^{[4]}^{[note 2]}