What's the result? $1/i=?$, where $i=\sqrt{-1}$ I just had my first math class in the university, and I understood everything pretty well, but I think I have misread this one because I read that the result is $-1$. Thanks for your answers!

Consider:
$$\dfrac{1}{i}=\dfrac{1}{i}\times\dfrac{i}{i}=\dfrac{i}{-1}=-i$$
However, the following argument would not work:
$$\dfrac{1}{i}=\dfrac{\sqrt{1}}{\sqrt{-1}}=\sqrt{\dfrac{1}{-1}}=\sqrt{-1}=\pm i .$$
The latter argument fails because $\frac{\sqrt{a}}{\sqrt{b}} \equiv \sqrt{\frac{a}{b}}$ holds (if and) only if $a,b>0.$
