Converting Complex Numbers from Cartesian to Polar Form

Complex numbers can be expressed either in Cartesian form

z = x + iy

or in polar form

z = r\textup{cis}\theta

wherever the situation is convenient.

In this video, I demonstrate how to convert a complex number from its Cartesian form to its polar form.

This is done simply by plotting the complex number as a point on the Argand plane, and then drawing a vector from the origin to that point. The angle that the vector makes with the horizontal real axis is the angle θ.

The magnitude of the vector |z| determines r.