Definition:Argument of Complex Number/Principal Argument

Definition
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 $\operatorname{Arg} \left({z}\right)$.

Note the capital $A$.

The standard practice is for $R$ to be $\left({-\pi \,.\,.\, \pi}\right]$.

This ensures that the principal argument is continuous on the real axis for positive numbers.

Also known as
Some sources give this as just the principal value.