Converting from Cartesian to Polar

Figure 3: Cartesian and polar representations of complex numbers in the complex plane.

Using trigonometric identities and the Pythagorean theorem, we can compute:

1. The Cartesian coordinates$(x, y)$ from the polar variables $r\angle\theta$:
   $$x = r\cos\theta$$   and$$\quad y=r\sin\theta$$

2. The polar coordinates from the Cartesian:
   $$r = \sqrt{x^2 + y^2}$$   and$$\quad \theta = \arctan\left(\frac{y}{x}\right)$$