Imaginary number

An imaginary number in mathematics is any number that contains the imaginary unit, defined as, <math>i^{2} = -1</math>

An imaginary number is of the form, <math>k i</math>, where k is a real number.

For example <math>\sqrt{-1}</math> has imaginary representation of

<math>\sqrt{-1}= \pm i</math>.

When a imaginary number is added to real number, they form a complex number. Imaginary numbers are mathematically useful because they ensure that every polynomial equation has a solution - for example, the equation <math>x^2+1=0</math> has no real solution.

The analysis of imaginary numbers forms the basis for the field of mathematics known as complex analysis.