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I am given the following riddle with complex numbers. But I can't figure what is wrong here:

$1=\sqrt{(-1)\cdot (-1)}=i\cdot i=-1$

onephys
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    Remember when they told you that $x^2=y^2\not\Rightarrow x=y$ ? That's basically why. –  Dec 28 '16 at 08:01
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    Because $(ab)^c = a^c\cdot b^c$ doesn't work for all combinations of bases and exponents, only some (for instance, positive bases and real exponents, or complex bases and integer exponents, or $e$ as base and complex exponents). One of the combinations that doesn't work is negative base and rational exponents. Alternatively, because one of the $\sqrt{-1}$ becomes $i$, and the other becomes $-i$; there is no way for the square root to tell the two apart, so how would it know which one to make two of? It's more natural that it makes one of each. – Arthur Dec 28 '16 at 08:01

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