The constant modulus algorithm (CMA) for blind equalization requires a separate carrier-recovery system for phase recovery. This letter mathematically analyzes a modified CMA, called the multimodulus algorithm (MMA), which may perform joint blind equalization and carrier recovery without the need for a separate carrier-recovery system for quadrature amplitude modulation signal constellations. The analyses focus on five aspects of the MMA: 1) derivation of the general formulation of the MMA cost function; 2) stationary points of the MMA; 3) desired global minima of the MMA; 4) unstable equilibria (saddle points) of the MMA; and 5) analytic verification of a discrete-time first-order phase-locked loop hidden inside the MMA, which is absent from the conventional CMA. Analysis results indicate that the MMA alone may be able to remove intersymbol interference and simultaneously correct the phase error, because it implicitly incorporates a phase-tracking loop, which automatically recovers carrier phase.