$$-1 = i\cdot i = \sqrt{-1}\sqrt{-1} = \sqrt{(-1)(-1)} = \sqrt{1} = 1$$
$$-1 = 1$$
Obviously, something is wrong here, but I can't put my finger on it.
How to solve this "contradiction"?
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1Branch cut of $\sqrt{z}$ – Gina Jun 25 '14 at 08:52
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1This has been asked here many times before... – Hans Lundmark Jun 25 '14 at 09:09
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How do you define $\sqrt{-1}$? If you set $\sqrt{-1}:=i$, then it is obvious that $\sqrt{-1 \cdot {-1}} \neq \sqrt{-1}^2$. – Filippo Sep 16 '23 at 16:07
