We propose the complex-valued product-unit residual network (CV-PURe), a novel neural architecture designed to jointly model magnitude and phase components with high fidelity. Unlike conventional complex-valued neural networks that predominantly employ summation-based operations and often struggle to capture nonlinear multiplicative dependencies, CV-PURe integrates complex-valued product units into residual blocks, enhancing its expressiveness while maintaining stable optimization via residual connections. We evaluate CV-PURe on the fastMRI single-coil knee dataset using undersampled k-space reconstruction as a benchmark. Experimental results show that CV-PURe consistently outperforms a standard complex-valued residual network (CV-ResNet) of comparable capacity in terms of structural similarity index (SSIM), peak signal-to-noise ratio (PSNR), and phase accuracy, while achieving a comparable normalized mean squared error (NMSE). Importantly, these improvements are achieved with approximately 30% fewer parameters than CV-ResNet, highlighting the parameter efficiency of the proposed architecture. These results demonstrate the effectiveness of incorporating product units into complex-valued networks and suggest the broader applicability of CV-PURe in signal reconstruction and other domains requiring accurate complex-valued representation, including medical imaging and diagnostics.