# How do you simplify # i^5#?

##### 2 Answers

Feb 10, 2016

This is the same as i

#### Explanation:

The complex i repeats after 4 powers

This can be seen with

i^1 = i

i^2 =

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.

Feb 10, 2016

#### Explanation:

Write as

But