I am trying not exactly to solve equation, but just change it from what is on right side to what is on left side. But I didn't do any math for years and can't remember what to.

$$\frac{1}{2jw(1+jw)}=\frac{-j(1-jw)}{2w(1+w^2)}$$

Here, $j^2=-1$.

If I am right, I should do something like this.

$$\frac{1}{(2jw(1+jw))}=\frac{(2jw(1-jw))}{(2jw(1+jw))}$$

But whatever I do I can't get what's shown above.

I will be thankful for any help.

## Best Answer

So, correct me if I'm wrong, but this equation seems to come from some electrical physics context? The reason I'm saying that is because it seems that $j$ is the imaginary unit (such that $j^2 = -1$), which is usually called $i$, except for some areas of physics (to not confuse it with intensity)If so, then a first step would be to nice that $\dfrac{1}{j} = -j$ (can you see why this is true?). And once you have that, you can do a common trick which is "multiplying by the conjugate".

Example: say you have an expression of the form $\dfrac{1}{a + bj}$, and you want to get a real denominator. You can achieve this by multiplying both the top and bottom by the

conjugateof $a + bj$, which is defined as $a - bj$ (see complex conjugate, keeping in mind that the article uses $i$ instead of $j$). I will let you perform the calculations for yourself (because that will help you understand what's going on), but this should be enough for you to finish the computations :)