Cross-corelation between complex baseband signals

Hi All,

I've a rather simple question related to the corelation between two
complex baseband signals. I haven't been able to figure it out yet, or find
an answer in any of the textbooks that I own. I've finally decided to
resort to the wisdom behind 'Ask-the-Audience' life line :)

So here is the question: If we compute cross-corelation between two
complex-baseband signals, we know that the real part of this
cross-corelation equals (excluding possibly a scale factor) the
cross-corelation between the corresponding passband signals. I am
interested in finding out how does the imaginary part of the
cross-corelation between two complex-baseband signals relate to the
cross-corelation between the passband signals.

Stated mathematically, if s(t) and r(t) are two passband signals, and
s_l(t) and r_l(t) their complex-baseband counterparts, then we know the
following.

Re[/s_l(t)r_l*(t)dt]=2/s(t)t(t)dt

where Re denotes the real part, * denotes conjugation, and / denotes the
integral sign. What I want to know is two things:

1- Starting from the LHS above, how do you go about proving its
equivalence to the RHS.

2- How does the RHS above change if we take the imaginary part of the
integral on the LHS. 

Any pointers will be greatly appreciated. Thanks.