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.

Resolving the

Rearranging them

Notice if we factorise out

Then with the formula we started with,

Voila! We are done and we have successfully derive our trigonometric form.