Anything which repeats on some periodic interval (e.g. a signal which repeats in time) can be represented geometrically as being defined with respect to uniform motion around a circle (sometimes there are physical circles involved, and sometimes it’s just an abstract circle).
Complex numbers (a two-part complex of a scalar part and a bivector part) and the complex logarithm/exponential are the natural formalism to use for describing uniform circular motion, and are therefore the natural formalism for any kind of periodic signal.
The way to teach this is to start with vectors in the plane, and then teach about geometric products/quotients of vectors (this is a subject called “geometric algebra” or “Clifford algebra”, and the basics are plenty accessible to high school students). All of the mystery is removed from complex numbers when they are taught this way.
Complex numbers (a two-part complex of a scalar part and a bivector part) and the complex logarithm/exponential are the natural formalism to use for describing uniform circular motion, and are therefore the natural formalism for any kind of periodic signal.
The way to teach this is to start with vectors in the plane, and then teach about geometric products/quotients of vectors (this is a subject called “geometric algebra” or “Clifford algebra”, and the basics are plenty accessible to high school students). All of the mystery is removed from complex numbers when they are taught this way.
http://www.shapeoperator.com/2016/12/12/sunset-geometry/