Surface nuclear magnetic resonance is a valuable technique that provides insight into the distribution of water content and relaxation time, thus revealing hydraulic properties in the subsurface. Recent research has introduced a new measurement layout that allows for time-efficient imaging of the 2D parameter distribution. Furthermore, for 1D investigations, it has been verified that complex data can provide improved resolution and depth penetration. In our research, we have developed an inverse modeling algorithm based on the QT-inversion scheme that uses the 2D complex magnetic resonance tomography data. We evaluate the uses and limitations of complex data for 2D investigations. By comparing resolution measures, we test this algorithm against state-of-the-art amplitude-based inverse modeling using resolution measures, a rigorous synthetic test, and a field example. Finally, we assess the impact of unknown conductivity and off-resonance excitation on the subsurface image and examined their limitations in field applications. We find that complex inversion is feasible in practice and provides superior results but demands precise knowledge of the true excitation frequency.