Why does capacitor impedance switch between +j and -j in J notation?

[lubo]

Homework Statement

We have a capacitor in parallel with an inductor. These are both in series with a resistor and capacitor.

Calculate the J notation Impedance of the network. I only want the initial basic solution.

The problem I have is that sometimes the J notation of C is -ve and sometimes +ve ?

Homework Equations

The Attempt at a Solution

Product/sum of the parallel cct:

jwL x 1/jwC/jwL*1/jwC This is the Inductor and capacitor impedance equation.

The above will be added to:

R -j(1/wC)

My question is therefore, why in the above example at product over sum would it be ok to say jwL x 1/jwC/jwL*1/jwC i.e. * a +ve 1/jwC

When below it I can add it to R and -j(1/wC)

I hope this makes sence, thanks for any help in advance.

 

[tiny-tim]

hi lubo!

My question is therefore, why in the above example at product over sum would it be ok to say jwL x 1/jwC/jwL*1/jwC i.e. * a +ve 1/jwC

When below it I can add it to R and -j(1/wC)

ah, but the first j is on the bottom, while the second is on the top …

and -j = 1/j ​