Ok hey guys,

I have sort of confused myself with the following:

$\displaystyle \frac{1}{i}\cdot\sqrt{\frac{1}{i}} = -i\left(\frac{1}{i}\right)^{\frac{1}{2}}=-\left(\frac{i^2}{i}\right)^{\frac{1}{2}}=-\sqrt{i}$

$\displaystyle \frac{1}{i}\cdot\sqrt{\frac{1}{i}} = \left(\frac{1}{i^3}\right)^{\frac{1}{2}} = \left(\frac{-i}{i^2}\right)^{1/2} = \sqrt{i}$.

So which one is correct?? And which operation is illegal/ill-defined?

Thanks a lot for the help.