In functional magnetic resonance imaging, voxel time courses after Fourier "image reconstruction" are complex valued as a result of phase errors due to magnetic field inhomogeneities. Nearly all fMRI studies derive functional "activation" based on magnitude time courses., Here we propose to directly model the entire complex or bivariate data rather than just the magnitude data. A nonlinear model is used to model activation on the complex signal, and a likelihood ratio test is derived to test for activation at each voxel. We investigate the performance of the model on a simulated dataset.