Question Number 127605 by pticantor last updated on 31/Dec/20
$${find}\:{arg}\left({z}\right) \\ $$$${where}\:\boldsymbol{{z}}=\mathrm{1}+\boldsymbol{{cos}}\alpha+{icos}\beta \\ $$
Answered by MJS_new last updated on 31/Dec/20
$$\mathrm{arg}\:\left(\mathrm{1}+\mathrm{cos}\:\alpha\:+\mathrm{i}\:\mathrm{cos}\:\beta\right)\:= \\ $$$$=\frac{\pi}{\mathrm{2}}\mathrm{sign}\:\left(\mathrm{cos}\:\beta\right)\:−\mathrm{arctan}\:\frac{\mathrm{1}+\mathrm{cos}\:\alpha}{\mathrm{cos}\:\beta} \\ $$