SOLUTION: Simplify i^41. (The answer in the back of the book is "i" -- I can't figure out how that answer is arrived at)

Question 140203This question is from textbook
: Simplify i^41. (The answer in the back of the book is "i" -- I can't figure out how that answer is arrived at) This question is from textbook

Answer by scott8148(6628) (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
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