I always stress to students the importance of the basics of complex numbers, that is
The three forms of the complex numbers. I have shown how to derive from the cartesian () to trigonometric form () form. But I seldom show students how to derive the polar form due to the rigor. So here we go. Lets first identify a few formulas from MF15.
Let us consider the polar form then.
Notice if we factorise out
Then with the formula we started with,
Voila! We are done and we have successfully derive our trigonometric form.