\begin{definition}[Definition:Argument of Complex Number/Principal Argument]
Let $R$ be the principal range of the complex numbers $\C$.
The unique value of $\theta$ in $R$ is known as the '''principal value of the argument''', or just '''principal argument''', of $z$.
This is denoted $\Arg z$.
Note the capital $A$.
The standard practice is for $R$ to be $\hointl {-\pi} \pi$.
This ensures that the '''principal argument''' is continuous on the real axis for positive numbers.
Thus, if $z$ is represented in the complex plane, the '''principal argument''' $\Arg z$ is intuitively defined as the angle which $z$ yields with the real ($y = 0$) axis.
{{MissingLinks|continuity of $\Arg z$ on the positive real axis}}
\end{definition}