# Math Help - Imaginary number proof problem

1. ## Imaginary number proof problem

I've just started imaginary numbers.
I'm trying to derive what the inverse of j is.
Where $j =\sqrt{-1}$

So I did the following:

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

Multiplied j by both sides.

$jz=1$

squared both sides

$-z^2 =1$

and by solving I get that z=j

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

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!

2. Originally Posted by elieh
Multiplied j by both sides $jz=1$ squared both sides $-z^2 =1$ and by solving I get that z=j
You should get $z=\pm j$ . Both are solutions of $-z^2 =1$ but only $z=-j$ is solution of $jz=1$. Why?. Because if we square both sides of an equation, can appear solutions that are not in the original one.

Another example: the only solution of $x=2$ is $2$ and the solutions of $x^2=4$ are $\pm 2$

3. Alright, Thank you!