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Judging by the output/GUI of their GPU profiler, "complex" there is more like "complex instructions", think f32 (floating point) ops that aren't additions and multiplications (and FMAs), but trigonometry, square roots, that sort of thing.

FFT plus some game stuff requires complex numbers to do partial rendering (e.g. do some now and then do more next frame - I've lost the link to the talk but IIRC EA did a talk on how they made a shader that emulates lights in the background that are out of focus (not Guassian but the actual cool effect as if it was a real camera))

bokeh?

edit: Found the article: https://www.ea.com/frostbite/news/circular-separable-convolu...

Holy crap thank you for finding it so fast, I've been searching for it for a while

quaternions? for rotations