  The IceCube-Gen2 Neutrino Observatory is proposed to extend the all-flavour
energy range of IceCube beyond PeV energies. It will comprise two key
components: I) An enlarged 8$\,$km$^3$ in-ice optical Cherenkov array to
measure the continuation of the IceCube astrophysical neutrino flux and improve
IceCube's point source sensitivity above $\sim\,$100$\,$TeV; and II) A very
large in-ice radio array with a surface area of about 500$\,$km$^2$. Radio
waves propagate through ice with a kilometer-long attenuation length, hence a
sparse radio array allows us to instrument a huge volume of ice to achieve a
sufficient sensitivity to detect neutrinos with energies above tens of PeV. The
different signal topologies for neutrino-induced events measured by the optical
and in-ice radio detector - the radio detector is mostly sensitive to the
cascades produced in the neutrino interaction, while the optical detector can
detect long-ranging muon and tau leptons with high accuracy - yield highly
complementary information. When detected in coincidence, these signals will
allow us to reconstruct the neutrino energy and arrival direction with high
fidelity. Furthermore, if events are detected in coincidence with a sufficient
rate, they resemble the unique opportunity to study systematic uncertainties
and to cross-calibrate both detector components. We present the expected rate
of coincidence events for 10 years of operation. Furthermore, we analyzed
possible detector optimizations to increase the coincidence rate.
