Theory If w=a+biw=a+biw=a+bi and Arg(w)=θ\operatorname{Arg}(w)=\thetaArg(w)=θ then (when appropriate): tanθ=ba\tan\theta=\frac{b}{a}tanθ=ab Also: Arg(z1z2)=Arg(z1)−Arg(z2) (mod 2π)\operatorname{Arg}\left(\frac{z_1}{z_2}\right)=\operatorname{Arg}(z_1)-\operatorname{Arg}(z_2)\ (\text{mod }2\pi)Arg(z2z1)=Arg(z1)−Arg(z2) (mod 2π)