(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Why is

[itex]\sqrt{\frac{1}{-1}} \neq \sqrt{\frac{-1}{1}}[/itex]

when quite obviously

[itex]\frac{1}{-1} = \frac{-1}{1}[/itex]

2. Relevant equations

N/A

3. The attempt at a solution

By the above inequality, I mean when one calculates [itex]\sqrt{\frac{1}{-1}}[/itex] as [itex]\frac{\sqrt{1}}{\sqrt{-1}}[/itex], and [itex]\sqrt{\frac{-1}{1}}[/itex] as [itex]\frac{\sqrt{-1}}{\sqrt{1}}[/itex]. Is it just that the "rule" which is taught at school for taking roots of fractions just doesn't always apply? That'd seem a little arbitrary.

This isn't a homework question, it's just something that popped into my mind while lying in bed, interspersed among much more interesting thoughts on isospin. I'm a final-year mathematician at university and I can't believe I'm asking such a basic question, but my migraine-addled brain won't let me work out why the above is true. It seems so trivial and pathetically simple that I must be missing something really obvious. Could someone shed some light and save me from my shame in asking such a question?

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# Homework Help: Misbehaving Imaginary Fractions

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