SOLUTION: How does (i+1)/(i-1) = -i

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Question 925788: How does (i+1)/(i-1) = -i
Found 2 solutions by Alan3354, richard1234:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How does (i+1)/(i-1) = -I
Multiply the NUM and DEN of the fraction by the conjugate of the DEN i+1
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(i+1)*(i+1)/((i-1)*(i+1)
= (i^2 + 2i + 1)/(i^2 - 1)
= (-1 + 2i + 1)/(-1 -1)
= 2i/(-2)
= -i

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
True if and only if i+1 = -i(i-1) (by multiplying both sides by i-1).

-i(i-1) = -i^2 + i = i+1, so equation is true