The behavior of complex numbers under certain operations is seemingly the same mechanism as is seen in physical systems. The style of notation used in engineering usually denotes a periodic motion or a compound of many waves.
Of interest for physics is that without the imaginary part, real numbers alone are a leaky abstraction. This structure extends to quaterions and octonions.
Indeed, I'm a physicist with a background in electronics, so I'm fluent in that stuff. The question is whether explaining complex numbers to a non physicist is really going to bring them any closer to physics.
Considering complex numbers lead to group theory and group theory may model atomic structure, this metaphysical correlation is at least worthy of note. It is almost as if we are living in a distortion of truth.
Of interest for physics is that without the imaginary part, real numbers alone are a leaky abstraction. This structure extends to quaterions and octonions.