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

Question

jdoe0001 · Answer

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

solomonzelman · Answer

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

solomonzelman · Answer

For all i^n

solomonzelman · Answer

I mean when n is divided by 4

solomonzelman · Answer

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

solomonzelman · Answer

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.   )

solomonzelman · Answer

Sorry for typing too much