# Simplify i^15

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

1. Remember that ” i power 2 ”  always equals to negative 1                                     i^2 = -1 .
2. Just like in case of real numbers, we have i^1 = i for complex numbers.
3. 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

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