Question

How do you simplify `i^5`?

Answer 1

This is the same as i

Explanation:

The complex i repeats after 4 powers

This can be seen with
i^1 = i
i^2 = `sqrt(-1)^2` = -1
i^3 = i^2 * i = -1 * i => -i
i^4 = i^2 * i^2 => -1 * -1 >>> 1

After this, we can take the mod 4 of the exponent
(in this case we can just do the next exponent, try it out and of course the answer will be the same as i ^ 1 )

Thus, the answer is i.

Answer 2

`"simplified "->" "i`

Explanation:

Write as `" "i^2xxi^2xxi`

But `i^2=-1" "`so we have:

`(-1)xx(-1)xxi" "=" "i`