How to simplify this power of i?

Question

i²⁶

Answer 1

The powers of "i" have only four values:

 

i¹ = i

i² = -1

i³ = -i

i⁴ = 1

 

They then repeat. So

 

i²⁶ = (i⁴)⁶ · i²

i²⁶ = -1

Answer 2

Hello Mirsha,

 

Here is a simple solution: i²=-1, therefore i²⁶= (i²)¹³ = (-1)¹³

Remember that (-1)^N is equal 1 for any even and -1 for any odd N. Therefore, (-1)¹³ = -1: the final answer is: i²⁶= -1.

 

Hope this will help.