The equation x2 + 1 = 0 has no real solution as x2 + 1 = 0 gives x2 = -1 and square of every real number is non-negative.
So, we need to extend the real number system to a larger system so that we can find the solution of the equation x2 = -1. In fact, the main objective is to solve the equation ax2 + bx + c = 0, where D = b2 - 4ac < 0, which is not possible in the system of real numbers.
A number of the form a + ib, where a and b are real numbers, is called a complex number, a is called the real part and b is called the imaginary part of the complex number.
A polynomial equation of n degree has n roots.