In a parallel circuit at its resonant frequency, the magnitude of the impedance will be at maximum since the respective reactive currents in the inductor and the capacitor cancel, leaving only the conduction of the resistor. As a mathematical consequence, since all the imaginary currents cancel, the impedance is purely real; hence the imaginary component of the impedance goes to zero as the frequency approaches resonance.
If, however, there is no resistor in parallel with the L and C, the magnitude of the impedance goes to infinity at resonance and its phase is undefined.
Ed