Kalid: you should really check out geometric algebra (a.k.a. Clifford algebra). It will give you a much deeper understanding of what i is and what the exponential function is, and how they generalize to higher dimensions and more complicated models, and it will help stitch together the weird inconsistent little fragments of understanding provided by imaginary numbers, quaternions, matrix algebra, Lie theory, differential forms, etc. into a more unified/cohesive model.

This is the model all high school and college students will be taught in 100 years, or perhaps even in 50 years, and it will prevent an enormous amount of confusion and misunderstanding. It’s already becoming the practical tool of choice in many geometric computing problems, and among niche groups of physicists.

”Reforming the Mathematical Language of Physics”, http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf

“Grassmann’s Vision” http://geocalc.clas.asu.edu/pdf/GrassmannsVision.pdf

“Imaginary Numbers are not Real” http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/Im...

“Geometric Algebra” http://arxiv.org/pdf/1205.5935v1.pdf (this one is a good place to go if you get stuck in another source).

(Or books might be better sources for going in depth. Search for New Foundations for Classical Mechanics, Geometric Algebra for Computer Science, Geometric Algebra for Physicists)

You’d also probably enjoy Hestenes’s work on modeling in physics teaching, e.g. http://modeling.asu.edu/R&E/ModelingThryPhysics.pdf http://worrydream.com/refs/Hestenes%20-%20Modeling%20games%2... http://modeling.asu.edu/R&E/Notes_on_Modeling_Theory.pdf http://modeling.asu.edu/R&E/Hestenes-ModelingTheory2007.pdf