Imaginary number

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

An imaginary number is of the form, $ki$, where k is a real number.

For example ${\sqrt {-1}}$ has imaginary representation of

${\sqrt {-1}}=\pm i$.

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 $x^{2}+1=0$ has no real solution.

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