Question

How do you simplify `i^1776`?

Answer 1

1

Explanation:

there is a pattern to powers of `i`:

`i^1 = i`

`i^2 = -1`

`i^3 = -i`

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

this cycle repeats for every power of `4`.

to simplify `i^1776`, we have to see if `1776` is divisible by `4`, and if not, find the remainder:

`1776/4 = 444`

there is no remainder, meaning that `i^1776` is in the fourth part of the pattern.

this also means that `i^1776` could be simplified as the answer to `i^4`, which is 1.