Question

How do I Simplify i^54

Answer 1

Answer:

$i^{54}=-1$

Step-by-step 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:

$i^{54}=-1$