Current deep learning based multi-channel speaker separation methods produce a monaural estimate of speaker signals captured by a reference microphone. This work presents a new multi-channel complex spectral mapping approach that simultaneously estimates the real and imaginary spectrograms of all speakers at all microphones. The proposed multi-input multi-output (MIMO) separation model uses a location-based training (LBT) criterion to resolve the permutation ambiguity in talker-independent speaker separation across microphones. Experimental results show that the proposed MIMO separation model outperforms a multi-input single-output (MISO) speaker separation model with monaural estimates. We also combine the MIMO separation model with a beamformer and a MISO speech enhancement model to further improve separation performance. The proposed approach achieves the state-of-the-art speaker separation on the open LibriCSS dataset.