imaginary number

The so-called imaginary number is by definition the square root of negative 1 and is denoted \(i\).

\[i^2=-1\]

Although it is called ‘imaginary’ this number is no more and no less an abstraction than many real numbers such as \(\pi\) or \(\sqrt{2}\). Its use was prompted by the need to deal with algebraic expressions such as \(x^2+1\) that have no root in the real numbers. Its introduction led directly to the development of the complex numbers and the quaternions, both of which are of great importance in both pure and applied mathematics.