So I had a discussion with my research advisor about resistance vs. impedance

It's a matter of choice, when you're talking about matched circuit, then impedance is the same thing as resistance since circuit is matched and complex values are canceled out , elsewhere resistance is a part of impedance as berkeman pointed out. So you might say that they are synonymous. But still, you're not making a fool out of yourself and you're correct when saying that impedance is carrying much more info than pure resistance .

Btw, I think of resistance as Z = R + j0 ;)

 

yeah you say it is 'purely resistive'

 

they are the same species of animal dimensionally, so they are commensurate meaning that they can be meaningfully added, subtracted, and, in some sense, compared. normally we think of the term "impedance" as a complex quantity where the real part is "resistance" and the imaginary part is "reactance". since you can only compare (< or >) real quantities, you can't compare a complex impedance to a real resistance unless you know for some reason that the imaginary part is zero, or you are comparing some function of the impedance, such as its magnitude or its real part, to the resistance.

many times specs on parts are expressed as "impedance" when the quantity is mostly or entirely real. the characteristic impedance of a transmission line or of free space would be examples.

 

Concepts can be confusing enough to someone new to EE.

However since you already were comfortable with the fact that impedance contains more than resistance (i.e. can also have inductive & capacitive reactance), a good stategy, would be just to let it go by. (as you are now thinking in retrospect)

If this was one of your profs, then this person 'holds the cards', in issuing grades. It's not a bad idea to stay on their good side. Beyond school, I also find it a useful, in building or maintaining rapport with people; not to press a point for the sake of being right.