Question

how to find the possible values of i^n where n is a positive integer

Answer 1

well... what's \(\large \bf i^2?\) anyway?

Answer 2

If n is divisible by 4 then i^n=1
If the reminder is 3, when n is divided by 3, then i^n = -i
If the reminder is 2, when n is divided by 3, then i^n = -1
If the reminder is 1, when n is divided by 3, then i^n = 1

Answer 3

For all i^n

Answer 4

I mean when n is divided by 4

Answer 5

\(\large\color{blue}{\rm i^{4s+1} =i}\)
\(\large\color{blue}{\rm i^{4s+2} =-1}\)
\(\large\color{blue}{\rm i^{4s+3} =-i}\)
\(\large\color{blue}{\rm i^{4s} =1}\)

Answer 6

For any positive, integer s.

( For \(\large\color{blue}{\rm i^{4s+2} =i}\) or \(\large\color{blue}{\rm i^{4s} =1}\) a negative integer would work too. )

Answer 7

Sorry for typing too much