  We apply the diagrammatic Monte Carlo approach to three-dimensional
Fermi-polaron systems with mass-imbalance, where an impurity interacts
resonantly with a noninteracting Fermi sea whose atoms have a different mass.
This method allows to go beyond frequently used variational techniques by
stochastically summing all relevant impurity Feynman diagrams up to a maximum
expansion order limited by the sign problem. Polaron energy and quasiparticle
residue can be accurately determined over a broad range of impurity masses.
Furthermore, the spectral function of an imbalanced polaron demonstrates the
stability of the quasiparticle and allows to locate in addition also the
repulsive polaron as an excited state. The quantitative exactness of
two-particle-hole wave-functions is investigated, resulting in a relative
lowering of polaronic energies in the mass-imbalance phase diagram. Tan's
contact coefficient for the mass-balanced polaron system is found in good
agreement with variational methods. Mass-imbalanced systems can be studied
experimentally by ultracold atom mixtures like $^6$Li-$^{40}$K.
