What is "imaginary unit"

n. (context complex analysis English) A complex number, usually denoted with ''i'', that is defined as $i^2\; =\; -1$

The imaginary unit or unit imaginary number () is a solution to the quadratic equation . Since there is no real number with this property, it extends the real numbers, and under the assumption that the familiar properties of addition and multiplication (namely closure, associativity, commutativity and distributivity) continue to hold for this extension, the complex numbers are generated by including it.

Imaginary numbers are an important mathematical concept, which extends the real number system to the complex number system , which in turn provides at least one root for every nonconstant polynomial . (See Algebraic closure and Fundamental theorem of algebra.) The term " imaginary" is used because there is no real number having a negative square.

There are two complex square roots of , namely and , just as there are two complex square roots of every real number other than zero, which has one double square root.

In contexts where is ambiguous or problematic, or the Greek is sometimes used (see ). In the disciplines of electrical engineering and control systems engineering, the imaginary unit is normally denoted by instead of , because is commonly used to denote electric current.

For the history of the imaginary unit, see .