All the numbers that we use in our calculations are real numbers and we know that the square of any real number is either a positive integer or zero but this is not true for  

x2=-1, because this denies the given axiom. For this the necessity of a set of numbers, that could satisfy the equation, was felt. This was resoveld when an imaginary number,mostly denoted by a symbol called iota, was introduced.

The complex number is a number consisting of two parts viz. real part and imaginary part. This helped the solution of many equations like:

x2+9=0

 previously, this equation had no solution, but now it can be solved with the help of complex numbers as;

Solution:

                x2-9*-1=0

or               x2-9i2=0 (because i2=-1)

or         (x-3i) (x+3i)=0

either, x-3i=0 or x+3i=0

So the solution set is {3i,-3i}

A number in the form of a+ib,where a and b are real numbers,is known as composite number.