Question

How do you simplify `5i ^ { - 1} + 5i ^ { - 2} + 5i ^ { - 3} + 5i ^ { - 4}`?

Answer 1

`5i^-1+5i^-2 +5i^-3+5i^-4 =0`

Explanation:

`i^2=-1 , i^3=-i`

`5i^-1+5i^-2 +5i^-3+5i^-4` or

`5i^-4(i^3+i^2 +i+1)` or

`5i^-4(-i-1+i+1) = 5i^-4*(0) =0` [Ans]