We investigate the origin of complex organic molecules (COMs) in the gas phase around the low-mass Class~0 protostar NGC1333-IRAS2A, to determine if the COM emission lines trace an embedded disk, shocks from the protostellar jet, or the warm inner parts of the protostellar envelope. In the framework of the CALYPSO (Continuum And Lines in Young ProtoStellar Objects) IRAM Plateau de Bure survey, we obtained large bandwidth spectra at sub-arcsecond resolution towards NGC 1333-IRAS2A. We identify the emission lines towards the central protostar and perform Gaussian fits to constrain the size of the emitting region for each of these lines, tracing various physical conditions and scales. The emission of numerous COMs such as methanol, ethylene glycol, and methyl formate is spatially resolved by our observations. This allows us to measure, for the first time, the size of the COM emission inside the protostellar envelope, finding that it originates from a region of radius 40-100 AU, centered on the NGC 1333-IRAS2A protostellar object. Our analysis shows no preferential elongation of the COM emission along the jet axis, and therefore does not support the hypothesis that COM emission arises from shocked envelope material at the base of the jet. Down to similar sizes, the dust continuum emission is well reproduced with a single envelope model, and therefore does not favor the hypothesis that COM emission arises from the thermal sublimation of grains embedded in a circumstellar disk. Finally, the typical scale $sim$60 AU observed for COM emission is consistent with the size of the inner envelope where $T_{rm{dust}} > 100$ K is expected. Our data therefore strongly suggest that the COM emission traces the hot corino in IRAS2A, i.e., the warm inner envelope material where the icy mantles of dust grains evaporate because they are passively heated by the central protostellar object.
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