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Old 01-25-2008   #1 (permalink)
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sanctus
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Very mean squareroot!

Have you already noticed that
\sqrt{-x}\cdot\sqrt{-y}=\pm\sqrt{xy}

Thing is that for half an hour I searched which of the two reasoponings is wrong:

1)
\sqrt{-x}\cdot\sqrt{-y}=\sqrt{(-1)\cdot x \cdot(-1)\cdot y}= \sqrt{xy}
Since -1*-1=+1

2)
\sqrt{-x}\cdot\sqrt{-y}= i\cdot\sqrt{x}\cdot i\cdot\sqrt{y}=i^2\sqrt{xy}=-\sqrt{xy}
Since i^2=-1

It took me as already said more than 3 min to figure it out, hope to you it isn't obvious at first read why both versions are right (and incomplete)...just so that I don't feel too stupid


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Last edited by sanctus; 01-28-2008 at 11:37 PM..
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