SOLUTION: i^41(book answer is i. I need help how to simplify)

Algebra ->  Algebra  -> Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: i^41(book answer is i. I need help how to simplify)      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   


Question 140206This question is from textbook
: i^41(book answer is i. I need help how to simplify)This question is from textbook

Answer by scott8148(5880) About Me  (Show Source):
You can put this solution on YOUR website!
well...you can multiply i by itself 41 times, or...

looking at powers of i __ i^0=1, i^1=i, i^2=-1, i^3=-i, i^4=1, i^5=i...

the pattern shows a 4-step cycle __ so divide the exponent by 4 and use the remainder

i^41=i^(41-40)=i^1=i