Excellent description. I’d maybe save quantum mechanics to last though, because many people have the same feeling of doubt about qm as op has about imaginary numbers. Let’s just say that periodic phenomena are much easier to describe using complex numbers. To give a sense of why that is you can say it’s because these need to shift energy back and forth between two different forms of energy, which is reflected in the two different kinds of numbers that make up a complex number - the real part and the imaginary part. A pendulum, for example, converts potential energy to kinetic energy and back again. Quantum mechanics is just one example of periodic phenomena.