SOLUTION: Find the power of i for i47.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the power of i for i47.      Log On


   

Question 19602: Find the power of i for i47.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Find the power of i for i47.
WE KNOW THAT
i^1=i
i^2=-1
i^3=i^2*i=-i
i^4=i^2*i^2=-1*-1=1..so first write the power as a multiple of 4 and remainder
here 47=4*11+3
so (i)^47=(i)^44*(i)^3 =+1*i^3=i^3=i^2*i=-i