Introduction
Complex numbers are an extension of the real numbers designed to solve equations that have no solutions within the realm of real numbers. The history of mathematics shows that man has been developing and enlarging his concept of number according to the saying that "Necessity is the mother of invention". In the remote past they started with the set of counting numbers and invented, by stages, the negative numbers, rational numbers, irrational numbers etc.
Since the square of a positive as well as a negative number is a positive number, the square root of a negative number does not exist in the realm of real numbers. Therefore, square roots of negative numbers were given no attention for centuries. However, properties of numbers involving square roots of negative numbers have been discussed in detail and such numbers have been found useful in many branches of pure, applied, financial and computational mathematics.