Question

What is `i^55` ?

Answer 1

`i^55 = -i`

Explanation:

Note that:

`i^4 = (-1)^2 = 1`

So:

`i^55 = i^((4*13)+2+1) = (i^4)^13 * i^2 * i = 1^13 * (-1) * i = -i`

More generally, for any integer `n` we have:

`i^(4n) = 1`

`i^(4n+1) = i`

`i^(4n+2) = -1`

`i^(4n+3) = -i`