# Complex Numbers

We know that the squares of real numbers is always non-negative, thus, there is no real number which can satisfy an equation of the type $x^{2}+k = 0$, where k > 0. in solving quadratic equations, we often get a square root of negative number as part of the values for roots.

The extraction of square root is not possible as no real numbers exists which when squared will yield a negative number.This shows the inadequacy of the real number system R. So, we need to widen the real number system so as to include square root of negative real number in such a manner that usual operations of addition, subtraction, multiplication and division and their related properties hold.

The new system is called the system of complex numbers and it include all the real numbers. In this section we will be learning more about complex numbers.