From what I understand about antennas, they have a certain impedance. At the antenna's resonant frequency, the capacitive and inductive reactances cancel and the reactive part of the antenna impedance is 0 ohms. However, there is also something called the radiation resistance that still exists at resonance (for a dipole, it is commonly 71 ohms). How can this be? At resonance, doesn't the feedpoint of the antenna look like a short circuit due to resonance? When the antenna is matched to a transmission line, do you use the reactance or the radiation resistance?
At resonance the imaginary part is zero, yes. Why is it surprising that there's still a real part?
Imagine a series (or parallel) RLC circuit. At the resonant frequency, the L and C impedance are equal and opposite. But you still have the R.
Another thing - the resistance that's left is not just radiation resistance, some of it is loss resistance - real resistive loss in the wires, etc.