("Imaginary Number" and "Imaginary numbers" redirect here. For the 2013 EP by The Maine, see Imaginary Numbers (EP).) An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i2 = −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. Originally coined in the 17th century as a derogatory term and regarded as fictitious or useless, the concept gained wide acceptance following the work of 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. Some authors use the term pure imaginary number to denote what is called here an imaginary number, and imaginary number to denote any complex number with non-zero imaginary part.

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