Question

How do I Simplify i^54

Answer 1

`i^(54)=-1`

Explanation:

First, recall the 4 basic imaginary exponents:

`i^1=i \text{, }i^2=-1\text{, }i^3=-1\text{ and } i^4=1`

So, we want to find:

`i^(54)`

This is the same as:

`=i^(52)\cdot i^2`

52 is 4 times 13. Thus:

`=(i^4)^(13)\cdot i^2`

Since we know that i to the fourth is 1:

`=(1)^(13)\cdot i^2`

Simplify:

`=i^2`

And this equals:

`=-1`

So:

`i^(54)=-1`