Question Number 48224 by gunawan last updated on 21/Nov/18
$${e}^{{z}} =\mathrm{1}−\sqrt{\mathrm{3}}{i} \\ $$$${z}=.. \\ $$
Answered by Smail last updated on 21/Nov/18
$${z}={ln}\left(\mathrm{1}−\sqrt{\mathrm{3}}{i}\right)={ln}\left(\mathrm{2}\left(\frac{\mathrm{1}}{\mathrm{2}}−{i}\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)\right) \\ $$$$={ln}\mathrm{2}+{ln}\left({e}^{−{i}\frac{\pi}{\mathrm{3}}} \right)={ln}\mathrm{2}−{i}\frac{\pi}{\mathrm{3}} \\ $$