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

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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(6628) 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