Pavs.rms=(Vs.rms^2)/4*Zs and Pavs.rms=(Vs.peak^2)/8*Zs so is Vs peak value or RMS value in the lecture? It seems to me it should be peak value and this results in my confusing about words "the factor of 4 instead of 8 is used since we are now dealing with complex power".
Again there is an Eq. Pin=0.5*(V1*I1'+V1'*I1) (eq.1), if the V1 and I1 are the peak values the Pin is peak value too.
Because Pin is power absorbed at the input of a two port network so it is Re(V1*I1') which is exactly the eq.1. But it should be RMS value.
Let's look at p.7 there is eq. Pin=Re(Yin)*(|V1|^2)/2 from this Pin is RMS power. So now I'm confusing are Pin, Pr and Pavs RMS or peak values....?
So, my guess is that Pin, Pr, Pavs are peak values.