i^61 ???
i^61
\(i^{61} = i^{60}\times i\\ = (i^{4})^{15} \times i\\ = [(i^2)^2]^{15} \times i\\ = [(-1)^2]^{15} \times i\\ = [1]^{15} \times i\\ = 1\times i\\ =i\)
Thanks, Melody for that answer....
Here's another way to evalute this for i raised to any "n" positve integer
n mod 4 = 1 → i
n mod 4 = 2 → -1
n mod 4 = 3 → - i
n mod 4 = 4 → 1
So
i^61 = 61 mod 4 = 1 → i just as Melody found !!!