*The solution to this type of problem is really simple, all we need to know are these three key points :*

*Remember that ” i power 2 ” always equals to negative 1**i^2 = -1 .**Just like in case of real numbers, we have i^1 = i for complex numbers.**When we have to simplify a large power of i,we break the down the power to smaller powers of 1 and 2 (that is i^1 and i^2 ) and then simplify using rule (1) and (2).*

**Solution:**

i^15 = ( i^14 ) * i

= { ( i ^ 2 ) ^ 7 } * i

= { (-1) ^ 7 } * i

= (-1) * i

= – i

Hence we say that -i is the simplified form of i ^ 15