I have some theories about why this could by wrong but I still haven't something that convinces me. What is wrong with this proof:
$ -1 = i^2 = i.i = \sqrt{-1}.\sqrt{-1} = \sqrt{(-1).(-1)}= \sqrt1 = 1 $
This would imply that:
$1 = -1$
Which is obviously false.
So my theory is that it's not a great idea to write $i = \sqrt{-1}$, but I'm not sure why...
Answer
The flaw is in assuming that the rule $\sqrt x\sqrt y=\sqrt{xy}$ holds with imaginary numbers. You just show us a counter-example.
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