$$i=\sqrt{-1}=\sqrt{\frac{1}{-1}}=\frac{1}{i}=\frac{-i^2}{i}=-i$$
I'm sure there is a mistake above but I can't figure out where. What's exactly wrong in the above situation & why?
2026-03-28 23:18:29.1774739909
What's wrong here?
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In general (at least as soon as complex numbers are involved), $\sqrt{ab}\ne\sqrt a\sqrt b$. Similarly $\sqrt{\frac1{-1}}\ne\frac{\sqrt 1}{\sqrt{-1}}$