SOLUTION: i^17 the only thing I know about this is that all things like this such as i^30 or i ^2 or i^7 all come up to one thing but I'm not sure what it is please help soon!

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: i^17 the only thing I know about this is that all things like this such as i^30 or i ^2 or i^7 all come up to one thing but I'm not sure what it is please help soon!       Log On


   

Question 162617: i^17
the only thing I know about this is that all things like this such as i^30 or i ^2 or i^7 all come up to one thing but I'm not sure what it is
please help soon!
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Evaluate:
i%5E17
Recall that:
i%5E1+=+%28sqrt%28-1%29%29%5E1=i
i%5E2+=+%28sqrt%28-1%29%29%5E2=-1
i%5E3+=+%28sqrt%28-1%29%29%5E3=-1%2Ai+=+-i
i%5E4+=+%28sqrt%28-1%29%29%5E4=%28-1%29%5E2+=+1
i%5E5+=+%28sqrt%28-1%29%29%5E5=1%2Ai+=+i
and so on...
So you can see that the sequence goes:
i, -1, -i, 1, i, -1, -1, 1,...as the exponent of i goes from:
1, 2, 3, 4, 5, 6, 7, 8,... every fourth power of i will be = 1, so if you divide the the given exponent of 17 (from i%5E17) by 4 you get 4 plus a remainder of 1, so i%5E16+=+1andi%5E17+=+i