Are complex numbers "magical?" So I'm reading Penrose, and all of sudden he explodes into excitement like a schoolgirl, fawning over complex numbers because they are "magical" and perform "miraculous" things, further spilling exclamation marks in the surrounding paragraphs about how he's only scratched the surface of "number magic!" What do you think? Are complex numbers "magical?" Do they perform "miracles?" Can someone show me a complex number equation that applies to the real world and performs a "miracle?"