The imaginary unit or unit imaginary number, denoted as i, is a mathematical concept which extends the real number system ℝ to the complex number system ℂ, which in turn provides at least one root for every polynomial P(x) (see algebraic closure and fundamental theorem of algebra). The imaginary unit's core property is that i2 = −1. The term "imaginary" is used because there is no real numberhaving a negative square.
There are in fact two complex square roots of −1, namely i and −i, just as there are two complex square roots of every other real number, except zero, which has one double square root.
In contexts where i is ambiguous or problematic, j or the Greek ι (see alternative notations) is sometimes used. In the disciplines of electrical engineering and control systems engineering, the imaginary unit is often denoted by j instead of i, because i is commonly used to denote electric current in these disciplines.
For a history of the imaginary unit, see Complex number: History.
