Complex argument

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The complex argument of a complex number $\scriptstyle z\,=\,a+bi\,=\,re^{i\theta }\,$ is

$\arg(z)=\arg(a+bi)=\arctan(b,a)=\arctan(\sin(\theta ),\cos(\theta ))=\theta ,\,$

where $\scriptstyle \theta \,$ is considered modulo $\scriptstyle 2\pi \,$, i.e. $\scriptstyle \theta \,\in \,[0,2\pi )\,$.

See also

• {{Atan2}} (arithmetic function template)