Complex numbers "are" (i.e. are isomorphic to, and can be conveniently thought of as) ratios of vectors in the Euclidean plane. http://geocalc.clas.asu.edu/pdf/

Complex numbers "are" (i.e. are isomorphic to, and can be conveniently thought of as) ratios of vectors in the Euclidean plane. http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf Any kind of physics involving >1 dimensional Euclidean space inherently involves complex numbers.