Simplify i22. possible choices are 1, - 1, i,-i

The answer to this question is 1

I assume you mean i^22

There’s a cycle i follows when being taken to a certain power, so let’s see what that is:

i^1 = i

i^2 = - 1

i^3 = - i

i^4 = 1

And i^5 = i, so our cycle repeats after every 4th power. To find i^22 then, we can divide 22 by 4 to obtain an answer of 5, with a remainder of 2. In other words, 22 = 4 (5) + 2

So, i^22 = i^[4 (5) + 2]

We can break that up into the product i^[4 (5) ] x i^2

We know that i^4 is 1, and 1^5 is still 1, so i^[4 (5) ] = 1; i^2 is simply - 1, so altogether, we find that

i^[4 (5) ] x i^2 = 1 x (-1) = - 1

Our answer then is - 1.