Independent Component Analysis (ICA) has been noted to be promising for the study of functional magnetic resonance imaging (fMRI) data also in its native complex-valued form. In this paper, we demonstrate the first successful application of group ICA to complex-valued fMRI data of an event-related paradigm. We show that networks associated with event-related responses as well as intrinsic fluctuations of hemodymamic activity can be extracted for data collected during an auditory oddball paradigm. The intrinsic networks are of particular interest due to their potential to study cognitive function and mental illness, including schizophrenia. More importantly, we show that analysis of fMRI data in its complex form can increase the sensitivity and specificity in the detection of activated brain regions both for event-related and block design paradigms when compared to magnitude-only applications. In addition, we introduce a novel fMRI phase-based visualization (FPV) technique to identify activated voxels such that the complex nature of the data is fully taken into account.