Question

How do you simplify `i^-12`?

Answer 1

`1`

Explanation:

You can use regular power rules:
`a^(-n) = 1/a^n`
`a^(n+m) = a^n * a^m`
`(a^n)^m = a^(n*m)`

And in addition, whenever you have the term `i^2`, always use `i^2 = -1`.

So, let me break it down in very small steps:

`i^(-12) = 1/i^12 = 1/i^(2*6) = 1/(i^2)^6 = 1 / (-1)^6 = 1 / (-1)^(2*3) = 1 / ((-1)^2)^3 = 1 / 1^3 = 1`

Alternatively, you can use `i^2 = -1 => i^4 = 1` and get there a bit quicker:
`i^(-12) = 1/i^12 = 1/i^(4 *3) = 1/(i^4)^3 = 1/1^3 = 1`