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Analog to Digital Conversion of Complex Signals

I'm working on a radar project. I'm using a VNA as the signal source and it outputs a complex signal  (Aeiφ ) . After I/Q demodulation  I get the inphase (I) and quadrature (Q) baseband signals which are also complex. While digitizing these two signal, how a two channel ADC operates? Does it take only the real parts ( I ) or the magnitudes  (I2+ Q)1/2 ?