Complex argument

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The complex argument of a complex number $z=a+bi=r{e}^{i\theta }$ is

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

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

See also

• {{Atan2}} (arithmetic function template)