Krishna
0

Step 1: Write the given equation

             1 + i^2 + i^4 + i^6 +..............+ i^{2n}


Step 1: Substitute the i^2 = -1 value in the equation.


               1 + i^2 + (i^2)^2 + (i^2)^3+................+ (i^2)^n


               1+ (-1) + (-1)^2 + (-1)^3 +...................+ (-1)^n


               1 - 1 + 1 - 1 +...........................+ (-1)^n


            The value depends on the n value

                    If n = even

                      The answer is = 1

                    If n = odd

                      The answer = -1