time-averaged power for a transmission line

How do you derive the formula for time-averaged power:
Pavg=1/2 * Re{VI*}
I know the general formula for time-averaged power that takes integral over 1 period, but how do you convert that formula into this? Where does the complex conjugate of I come from?

Thanks a lot.

Power(t)=V(t)*I(t). If V and I are not DC, for example sinusoidal AC then active power(average power), reactive power, apperant power concepts emerge. Lets say V=A*cos(wt) and I=B*cos(wt+fi).
Power(t)=A*B*cos(wt)*cos(wt+fi). This is instantaneous power, If you want to find average of it, it is enough to find one period's average only. Period is 2*pi*1/w.
If you integrate cos(wt)*cos(wt+fi) product and take its average(by dividing pediod) you will end up with 0.5*cos(fi). Therefore average of A*B*cos(wt)*cos(wt+fi) becomes 0.5*A*B*cos(fi).
Wht about Pavg=1/2 * Re{VI*} ? This is called complex power.
In AC analysis we represent our sinusoidals with an complex number(phasors) to make our analysis easier. That power expression is written for phasor representation. VI* gives you a complex number whose magnitude is A*B and pahse is fi(difference btw V and I). If you take real part of it you will find A*B*cos(fi), same as above time domain derivation.

Hi serhann,
Complex representation confused me too. The thing to remember is that the power formula P = 1/2 Re(V I*) is to calculate the time averaged power when you are representing V and I as phasors rather than actual time functions. Phasors are used since doing that makes it really easy to handle phase and the time to phasor transformation representation i.e. Vo cos(wt+ phi ) -> Vo exp(j phi ) can be used in all Linear Systems equations since KVL and KCL are linear equations. So you can do all KVL KCL manipulations using phasors and in the end take the real part to get the actual answer and that will be corrent. But when it comes to calculating power which actually multiplies 2 quantities then the phasor system stops matching the actual real results in time domain. So now you have to go ahead and find a particular equation for the phasor system that would give us the correct answer for the power. And that happens to be 1/2xRe(V I*)
Check out the derivation I have attached for a better understanding on why do we need to take the conjugate and what if we don't.

Thank you very much ferdem and aryajur. Now, I understand where the formula comes from. Derivation has been truly helpful.