I've just started imaginary numbers.

I'm trying to derive what the inverse of j is.

Where $\displaystyle j =\sqrt{-1}$

So I did the following:

$\displaystyle \frac{1}{j}=\frac{z}{1}$

Multiplied j by both sides.

$\displaystyle jz=1 $

squared both sides

$\displaystyle -z^2 =1 $

and by solving I get that z=j

which is obviously wrong since $\displaystyle j^2 \neq 1 $

Any insights on what I'm over looking?

I derived it another why, but I want to know why this approach isn't working.

Thanks!