TITLE: proof for $\frac{1}{i} = -i$?
QUESTION [8 upvotes]: My physical chemistry textbook seems to be making the implicit assumption that $\cfrac{1}{i} = -i$.
I'm not sure how this is valid. Here is the snippet of relevant steps:
$\cfrac{i\hbar}{f(t)}$$\cfrac{df(t)}{dt}$$ = E$ ---I can see multiplying by $f(t)$ here and dividing by $i\hbar$
$\cfrac{df(t)}{dt} = $$ -\cfrac{i}{\hbar}$$Ef(t)$ 
[If you're wondering,this is part of the time-dependent Schrodinger equation.]

REPLY [5 votes]: Another proof is that for any number $n$ its inverse is the number $\frac 1n $ such that $n \times \frac 1n=1$ and we have that:
$$i\times -i=-(i\times i)=-(-1)=1$$
So we can conclude that:
$$\frac 1i=-i$$