  We calculate the zero-temperature equation of state of mass-imbalanced
resonant Fermi gases in an ab initio fashion, by implementing the recent
proposal of imaginary-valued mass difference to bypass the sign problem in
lattice Monte Carlo calculations. The fully non-perturbative results thus
obtained are analytically continued to real mass imbalance to yield the
physical equation of state, providing predictions for upcoming experiments with
mass-imbalanced atomic Fermi gases. In addition, we present an exact relation
for the rate of change of the equation of state at small mass imbalances,
showing that it is fully determined by the energy of the mass-balanced system.
