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The statistical distribution and evolution of key properties (e.g. accretionrate, mass, or spin) of active galactic nuclei (AGN), remain an open debate inastrophysics. The ESA Euclid space mission, launched on July 1st 2023, promisesa breakthrough in this field. We create detailed mock catalogues of AGNspectra, from the rest-frame near-infrared down to the ultraviolet, includingemission lines, to simulate what Euclid will observe for both obscured (type 2)and unobscured (type 1) AGN. We concentrate on the red grisms of the NISPinstrument, which will be used for the wide-field survey, opening a new windowfor spectroscopic AGN studies in the near-infrared. We quantify the efficiencyin the redshift determination as well as in retrieving the emission line fluxof the H$\alpha$+[NII] complex as Euclid is mainly focused on this emissionline as it is expected to be the brightest one in the probed redshift range.Spectroscopic redshifts are measured for 83% of the simulated AGN in theinterval where the H$\alpha$+[NII] is visible (0.89<z<1.83 at a line flux$>2x10^{-16}$ erg s$^{-1}$ cm$^{-2}$, encompassing the peak of AGN activity at$z\simeq 1-1.5$) within the spectral coverage of the red grism. Outside thisredshift range, the measurement efficiency decreases significantly. Overall, aspectroscopic redshift is correctly determined for ~90% of type 2 AGN down toan emission line flux of $3x10^{-16}$ erg s$^{-1}$ cm$^{-2}$, and for type 1AGN down to $8.5x10^{-16}$ erg s$^{-1}$ cm$^{-2}$. Recovered black hole massvalues show a small offset with respect to the input values ~10%, but theagreement is good overall. With such a high spectroscopic coverage at z<2, wewill be able to measure AGN demography, scaling relations, and clustering fromthe epoch of the peak of AGN activity down to the present-day Universe forhundreds of thousand AGN with homogeneous spectroscopic information.

Euclid preparation. Spectroscopy of active galactic nuclei with NISP