Ultrafast ultrasound imaging remains an active area of interest in the ultrasound community due to its ultra-high frame rates. Recently, a wide variety of studies based on deep learning have sought to improve ultrafast ultrasound imaging. Most of these approaches have been performed on radio frequency (RF) signals. However, inphase/quadrature (I/Q) digital beamformers are now widely used as low-cost strategies. In this work, we used complex convolutional neural networks for reconstruction of ultrasound images from I/Q signals. We recently described a convolutional neural network architecture called ID-Net, which exploited an inception layer designed for reconstruction of RF diverging-wave ultrasound images. In the present study, we derive the complex equivalent of this network; i.e., the Complex-valued Inception for Diverging-wave Network (CID-Net) that operates on I/Q data. We provide experimental evidence that CID-Net provides the same image quality as that obtained from RF-trained convolutional neural networks; i.e., using only three I/Q images, the CID-Net produces high-quality images that can compete with those obtained by coherently compounding 31 RF images. Moreover, we show that CID-Net outperforms the straightforward architecture that consists of processing the real and imaginary parts of the I/Q signal separately, which thereby indicates the importance of consistently processing the I/Q signals using a network that exploits the complex nature of such signals.