Capacity bounds are studied for the multiple-antenna complex Gaussian relay channel with t1 transmitting antennas at the sender, r2 receiving and t2 transmitting antennas at the relay, and r3 receiving antennas at the receiver. It is shown that the partial decode-forward coding scheme achieves within min(t1,r2) bits from the cutset bound and at least one half of the cutset bound, establishing a good approximate expression of the capacity. A similar additive gap of min(t1 + t2, r3) + r2 bits is shown to be achieved by the compress-forward coding scheme.