Question

What is the value of `i^-39`?

Write this in form of `a + bi`

Answer 1

`i^(-39) = i`

Explanation:

We know that:

`i^4 = 1`

so that in general:

`i^(4k) = (i^4)^k = 1` for any `k in ZZ`

Now:

`i^(-39) = i^(-40+1) = i^(-40)i = (i^4)^(-10) i = i`