(Vout/Vin) for RC/RL/RLC Circuits

Hey guys,
I think I finally understand how to tackle RC, RL, or RLC circuits. However, I am not entirely clear on some of the derivations I have been looking at. It is my understanding that j is an operator that signifies a shift of 90 degrees - and that in an equation j = sqrt [-1]

I have found that using the voltage divider rule instead of using complex conjugates for these circuits is much easier. But I am having a slight problem with j. I have attached the derivation below.


When finding the magnitude of Vc/Vin, and the whole expression is squared (and then sqrt) - why doesn't the j leave a -1?

Because you don't square the j.

The magnitude of a complex number a+jb=sqrt[(a^2)+(b^2)]

hello mzsyed85,

By meaning magnitude we are finding te distance of the point from the origin and here the point is (1,wrc) and we should not include j because it tells us that the point lies in a complex plane and then we are finding the magnitude similar to pythagoras theorem (sqrt(a^2 + b^2) = c where c is the magnitude and a and b are the points

I don't deserve such help. Thanks for clearing that up for me