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From Citizendium, the Citizens' Compendium

In mathematics, an imaginary number is a complex number that is not real. The term is not generally used because complex numbers (e.g., 3 + 4i) have two components, a real part (in this case 3), and an imaginary part (in this case 4). A complex number is said to be real if the imaginary part is 0, and in all other cases it is non-real. In most cases, when people speak of imaginary numbers, they are not referring to complex numbers which are not real, but complex numbers with the real part of 0. For clarity, such numbers are usually called pure imaginary.

The terms real and imaginary are misnomers; they should not be taken literally.

For more information, see Complex number.