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-1 is not 1, so where is the mistake?
Simple Complex Number Problem: 1 = -1

Well, I remembered this after having Algebra II a year ago, is it possible that this is a valid proof that $1 = -1$?

$ 1 = \sqrt{1} = \sqrt{-1\cdot-1} = \sqrt{-1} \cdot \sqrt{-1} = i \cdot i = i^2 = -1 $

$ \therefore 1 = -1 $

So is this actually fully valid? Or can it be disproved?

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    $\sqrt{-1\cdot-1}\neq\sqrt{-1}\sqrt{-1}$. If we replace $-1$ with $-2$ (just for good measure) and simplify, we arrive at $2\neq\sqrt{-2}\sqrt{-2}$, which seems reasonable enough.2012-11-05

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I think the problem is between $\sqrt{ -1 \dot{} -1 }$ and $\sqrt{-1} \dot{} \sqrt{-1}$.