SOLUTION: (-1- square root 7i) and (-1+square root 7i)

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Question 413608: (-1- square root 7i) and (-1+square root 7i)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
I assume the i's are not inside the square roots. (If they are, then you might be able to figure the solution from the solution below anyway.)

%28-1-sqrt%287%29%2Ai%29%28-1%2Bsqrt%287%29%2Ai%29
You could use FOIL on this. But it will be faster if we recognize that this expression fits the pattern: %28a-b%29%28a%2Bb%29+=+a%5E2-b%5E2 with the "a" being -1 and the "b" being sqrt%287%29%2Ai. So from the pattern we know that the product will be a%5E2-b%5E2:
%28-1%29%5E2+-+%28sqrt%287%29%2Ai%29%5E2
which simplifies as follows:
1+-+%28sqrt%287%29%29%5E2%2Ai%5E2
And since %28sqrt%287%29%29%5E2+=+7 and i%5E2+=+-1 this becomes:
1 - (7)(-1)
which simplifies:
1 - (-7)
1 + 7
8
Note: If you use FOIL instead and use it correctly, you will still get 8 for the simplified answer.