SOLUTION: What is (i)^42.....is it (-1)?

Question 17345: What is (i)^42.....is it (-1)?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
i)^42.....is it (-1)?
we know that
i=i
i^2=-1
i^3=i^2*i=-1*i=-i
i^4=(i^2)^2=1...etc
so we see that if the power is even number then the answer is 1 or -1 and if power is odd number then the answer is i or -i
now in the problem i^42 we know that 42 is even number .so answer is 1 or -1 ..now to find whether it is +1 or -1 ..we have to find it is even number divisible by 4 or not. if it is divisible by 4 the answer is +1 other wise the answer is -1.
here 42 is not divisible by 4 ..so the answer is -1
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