Recent studies have shown convolutional neural networks (CNNs) can be trained to perform modal decomposition using intensity images of optical fields. A fundamental limitation of these techniques is that the modal phases cannot be uniquely calculated using a single intensity image. The knowledge of modal phases is crucial for wavefront sensing, alignment, and mode matching applications. Heterodyne imaging techniques can provide images of the transverse complex amplitude and phase profiles of laser beams at high resolutions and frame rates. In this work, we train a CNN to perform modal decomposition using simulated heterodyne images, allowing the complete modal phases to be predicted. This is, to our knowledge, the first machine learning decomposition scheme to utilize complex phase information to perform modal decomposition. We compare our network with a traditional overlap integral and center-of-mass centering algorithm and show that it is both less sensitive to beam centering and on average more accurate in our simulated images.