- #1
a.powell
- 9
- 0
Homework Statement
Why is
[itex]\sqrt{\frac{1}{-1}} \neq \sqrt{\frac{-1}{1}}[/itex]
when quite obviously
[itex]\frac{1}{-1} = \frac{-1}{1}[/itex]
Homework Equations
N/A
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?