X-ray and mid-infrared emission are signposts of the accretion of matter onto the supermassive black holes that reside at the centres of most galaxies. As a major step towards understanding accreting supermassive black holes and their role in the evolution of galaxies, we will use the 4MOST multi-object spectrograph to provide a highly complete census of active galactic nuclei over a large fraction of the extragalactic sky observed in X-rays by eROSITA that is visible to 4MOST. We will systematically follow up all eROSITA point-like extragalactic X-ray sources (mostly active galactic nuclei), and complement them with a heavily obscured active galactic nuclei selection approach using mid-infrared data from the Wide-field Infrared Survey Explorer (WISE). The X-ray and mid-infrared flux limits of eROSITA and WISE are well matched to the spectroscopic capabilities of a 4-metre-class telescope, allowing us to reach completeness levels of ~80-90% for all X-ray selected active galactic nuclei with fluxes $f_{0.5-2 {rm keV}} > 10^{-14}$ erg s$^{-1}$ cm$^{-2}$; this is about a factor of 30 deeper than the ROSAT all-sky survey. With these data we will determine the physical properties (redshift, luminosity, line emission strength, masses, etc.) of up to one million supermassive black holes, constrain their cosmic evolution and clustering properties, and explore the connection between active galactic nuclei and large-scale structure over redshifts $0 le z le 6$.
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