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We introduce a family of complex modulation signals that are generated as patterns over the real and imaginary plane for characterization of coherent optical receivers. The properties of the complex signals can be predicted from first principles, enabling quantitative comparisons between measurement and theory. An optical heterodyne technique with phase-locked loops for frequency control and narrow-band lasers was used to create the known signals, providing temporal stability and ease of operation. The modulation patterns could be made arbitrarily intricate simply by selection of the heterodyne frequencies, with no hardware modifications. The technique is capable of generating signals with frequencies of more than 100 GHz. A real-time optical modulation analyzer was used to visualize the modulation patterns and illustrate their properties. In turn, we used the modulation patterns to characterize the coherent receiver within the modulation analyzer, thereby examining its demodulation algorithm, software processing, digital filtering, and detector gain balance. By working with known modulation patterns, we were able to create an error vector waveform to allow quantitative evaluation of measured signals as they spanned the complex plane.