We report here the first measurements of the complex modulus of the isolated red blood cell (RBC). Because the RBC is often larger than capillary diameter, important determinants of microcirculatory function are RBC deformability and its changes with pathologies such as sickle cell disease and malaria. A functionalized ferrimagnetic microbead was attached to the membrane of healthy RBC and then subjected to an oscillatory magnetic field. The resulting torque caused cell deformation. From the oscillatory forcing and resulting bead motions, which were tracked optically, we computed elastic and frictional moduli, g' and g", from 0.1 to 100 Hz. g' was nearly frequency independent and dominated the response at all but the highest frequencies measured. Over three frequency decades g" increased as a power law with an exponent of 0.64, a result not predicted by any simple model. These data suggest that RBC relaxation times that have been reported previously, and any models that rest upon them, are artifactual; the artifact, we suggest, arises from forcing to an exponential fit data of limited temporal duration. A linear range of response was observed but as forcing amplitude increased nonlinearities became clearly apparent. A finite element model suggests that membrane bending was localized to the vicinity of the bead and dominated membrane shear. While the mechanisms accounting for these RBC dynamics remain unclear, methods described here establish new avenues for the exploration of connections among the mechanical, chemical and biological characteristics of the RBC in health and disease.