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Simple Definitions

The most important electronics terms, demystified in one place.

Imaginary numbers

Our Take

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 i2 = −1.[1] The square of an imaginary number bi is −b2. For example, 5i 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]

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