SOLUTION: What is i83= Thank you. I need before 12:00 and could explain why the pattern of imaginary numbers repeat themselves? It would really help me on my test tommorrow!!!!!!!!!!!!1

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: What is i83= Thank you. I need before 12:00 and could explain why the pattern of imaginary numbers repeat themselves? It would really help me on my test tommorrow!!!!!!!!!!!!1      Log On


   

Question 14062: What is i83= Thank you. I need before 12:00 and could explain why the pattern of imaginary numbers repeat themselves? It would really help me on my test tommorrow!!!!!!!!!!!!1
Answer by bam878s(77) About Me  (Show Source):
You can put this solution on YOUR website!
note i%5E83=i%5E80%2Ai%5E3.
we have i%5E80+%2A+%28-i%29 since i^3 = -i.
and i%5E80=%28i%5E2%29%5E40.
we know i%5E2 = -1.
so what we have %28-1%29%5E40+%2A+%28-i%29.
we know %28-1%29%5Eevenpower=1
and %28-1%29%5Eoddpower= -1.
since 40 is even %28-1%29%5E40 = 1
so we have 1%2A%28-i%29 = -i.
Hope this helps you again.