What is Argument, trigonometric and exponential forms?

Let $z \neq 0$. An argument of $z$, written $\Arg(z)$, is any measure $\theta$ of the angle from the positive real axis to the ray $OM$; it is defined up to $2k\pi$. Writing $r = \abs z$,

Introducing the notation

this becomes the exponential form $z = r\,\eu^{\iu\theta}$.