SOLUTION: i^-19= here are my choices 1, -1, i, -i any help would be appreaciated, thanks!

Algebra ->  Square-cubic-other-roots -> SOLUTION: i^-19= here are my choices 1, -1, i, -i any help would be appreaciated, thanks!       Log On


   

Question 181243: i^-19= here are my choices 1, -1, i, -i
any help would be appreaciated, thanks!
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
i=i
i^2=-1
i^3=-i
i^4=1
:
so any multiple of i^4=1
:
divide 19 by 4 =4 and 3 left over so
:
i%5E19=i%5E16%2Ai%5E3 = 1(-i)=-i
:
i%5E-19+=1%2F%28i%5E19%29=1%2F%28-i%29multiply top and bottom by -i=-i%2F-1=i
:
answer is i