  We study the pseudo-spin density response of a disordered two-dimensional
spin-polarized Bose gas of exciton polaritons to weak alternating magnetic
field, assuming that one of the spin states of the doublet is macroscopically
occupied and Bose-condensed while the occupation of the other state remains
much smaller. We calculate spatial and temporal dispersions of spin
susceptibility of the gas taking into account spin-flip processes due to the
transverse-longitudinal splitting. Further, we use the Bogoliubov theory of
weakly-interacting gases and show that the time-dependent magnetic field power
absorption exhibits double resonance structure corresponding to two particle
spin states (contrast to paramagnetic resonance in regular spin-polarized
electron gas). We analyze the widths of these resonances caused by scattering
on the disorder and show that, in contrast with the ballistic regime, in the
presence of impurities, the polariton scattering on them is twofold: scattering
on the impurity potential directly and scattering on the spatially fluctuating
condensate density caused by the disorder. As a result, the width of the
resonance associated with the Bose-condensed spin state can be surprizingly
narrow in comparison with the width of the resonance associated with the
non-condensed state.
