Question

How do you simplify `i^-6`?

Answer 1

`-1`

Explanation:

First, recognize the powers of `i`:

`{(i=sqrt(-1)),(i^2=(sqrt(-1))^2=-1),(i^4=(i^2)^2=(-1)^2=1):}`

Note that `i^-6=1/i^6`.

`i^-6=1/i^6=1/(i^4(i^2))=1/(1(-1))=-1`