argument (of a complex number)

Which way a complex number points from the origin — the angle in its polar form.

For a nonzero complex number $z=a+bi$ , the argument, written $\arg(z)=\theta$ , is the angle the segment from $0$ to $z$ makes with the positive real axis, measured the same way as any angle in standard position. An argument is never unique — adding any whole multiple of $2\pi$ to $\theta$ names the same direction — so a convention like $[0,2\pi)$ is usually chosen to report one representative value.