Question

simplify i^31 (click photo for options)

Answer 1

i^1=i
i^2=-1
i^3=-1*i
1^4=-1*-1=1

this repeats itself over and over again:
i^5=-1*-1*i=i
..

31/4=6 with a remainder of 3, so for i^31 it repeated 6 times and then it is the third entry of the table:

so we know i^31=i^3 -> look it up above =-1*i=-i=3rd option