SOLUTION: Find the power of i (-i)^42 A) 1 B)None C) 42i D)i E) -i

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Question 713186: Find the power of i
(-i)^42
A) 1 B)None C) 42i D)i E) -i
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28-i%29%5E42
First, we can make things easier if we separate the "-" from the "i". Using the fact that -i = -1*i and a rule for exponents, %28a%2Ab%29%5En+=+a%5En%2Ab%5En we can rewrite the expression as:
%28-1%29%5E42%2Ai%5E42
Since (-1)*(-1) = 1 and since %28-1%29%5E42 is just 21 pairs of (-1)*(-1), %28-1%29%5E42+=+1 So the expression is now down to:
i%5E42

Since i+=+sqrt%28-1%29, i%5E2+=+-1. And since i%5E4+=+%28i%5E2%29%5E2, i%5E4+=+%28-1%29%5E2+=+1 Since i%5E42 is 10 sets of i%5E4 and one i%5E2, i%5E4+=+-1:
i%5E42+=+%28i%5E4%29%5E10%2Ai%5E2+=+1%5E10%2A%28-1%29+=+-1

So the answer to the problem is B (None).