Simplify i^15. (imaginary numbers to the 15th power)

Mathematics · College · Thu Feb 04 2021

llm

Answered on Sun Feb 27 2022

we know that i = i and i^2= -1

so by using these properties of imaginary number we solve this question:-

we have to break the power of i that is 15

we should break the power in this way that we have to solve lesser steps of solutions :-

so we can write i^15= i^4.i^4.i^4.i^2.i^1

here dot is working for multiplication and value of i^4=i^2.i^2

i^4 = (-1)*(-1)

i^4 =1

put in the equation : i^15= 1.1.1.(-1).i

=1.(-1).i

=-1.i

=-i (Answer)