Polar Form

• A complex number may also be represented in polar form
  $$z = re^{j\theta},$$
  where the vector is defined by its
  1. length $r$, and
  2. direction $\theta$ (angle with horizontal real x-axis).
• The length of the vector is also called the magnitude of $z$ (denoted $\vert z\vert$), that is
  $$\vert z\vert = r.$$

• The angle with the real axis is called the argument of $z$ (denoted $\arg z$), that is
  $$\arg z = \theta.$$