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# Complex argument

The complex argument of a complex number ${\displaystyle \scriptstyle z\,=\,a+bi\,=\,re^{i\theta }\,}$ is
${\displaystyle \arg(z)=\arg(a+bi)=\arctan(b,a)=\arctan(\sin(\theta ),\cos(\theta ))=\theta ,\,}$
where ${\displaystyle \scriptstyle \theta \,}$ is considered modulo ${\displaystyle \scriptstyle 2\pi \,}$, i.e. ${\displaystyle \scriptstyle \theta \,\in \,[0,2\pi )\,}$.