SOLUTION: Hi could you please help me with this? i^34 Is it 34? I know i=-1 right? Thank you

Algebra ->  Real-numbers -> SOLUTION: Hi could you please help me with this? i^34 Is it 34? I know i=-1 right? Thank you      Log On


   

Question 45882: Hi could you please help me with this?
i^34
Is it 34? I know i=-1 right?
Thank you
Found 2 solutions by Nate, Earlsdon:
Answer by Nate(3500) About Me  (Show Source):
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can work this out for yourself:
i+=+sqrt%28-1%29 = i
i%5E2+=+%28sqrt%28-1%29%29%5E2 = -1
i%5E3+=+-1sqrt%28-1%29 = -1%2Ai = -i
i%5E4+=+%28i%5E2%29%5E2 = %28-1%29%5E2+=+1
i%5E5+=+%28i%5E4%29%2Ai = i
As you can see, i%5En goes around in circles, starting with i when n = 1...as follows.
n = 1..i%5E1+=+i
n = 2..i%5E2+=+-1
n = 3..i%5E3+=+-i
n = 4..i%5E4+=+1
n = 5..i%5E5+=+i now we're back to where we started.
So to find the value of i%5E34, you divide 34 by 4 and then take the remainder (it's 2 in this case) and find i%5E2 from the above table.
i%5E34+=+-1