INTEGRAL POWERS OF IOTA ( i )
What is the solution of the equation x 2 + 1 = 0? In fact we don’t have any solution to the given equation in the system of real numbers. Why? Because x 2 + 1 = 0 gives x 2 = -1 and square of every real number is non-negative. Then, what could we do? We need to extend the real number system to a larger system to find the solution of the equation x 2 + 1 = 0. In general, we have to find the solution of the equation ax 2 + bx + c = 0, where D = b 2 – 4ac < 0. Euler was the first mathematician to introduce the symbol i ( Iota ) for the square root of -1, i.e. solution of the equation x 2 + 1 = 0. Now, we have i = √-1 i 2 = -1 i 3 = i 2 * i = -i i 4 = ( i 2 ) 2 = ( -1 ) 2 = 1