Comment by zkmon

This is just scratch on the surface.

* Enter quaternions; things get more profound.

* Investigate why multiplicative inverse of i is same as its additive inverse.

* Experiment with (1+i)/(1-i).

* Explore why i^i is real number.

* Ask why multiplication should become an addition for angles.

* Inquire the significance of the unit circle in the complex plane.

* Think bout Riemann's sphere.

* Understand how all this adds helps wave functions and quantum amplitudes.