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 $\Arg z$.

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.

Also known as

Some sources give this as just the principal value.

Linguistic Note

The word principal is an adjective which means main.

Do not confuse with the word principle, which is a noun.