Question Number 176549 by doline last updated on 21/Sep/22
$${donner}\:{la}\:{forme}\:{trigonometrique}\:{de}\:\mathrm{1}/\mathrm{4}\left({cos}\Pi/\mathrm{9}+{isin}\Pi/\mathrm{9}\right) \\ $$
Answered by Ar Brandon last updated on 21/Sep/22
$$\frac{\mathrm{1}}{\mathrm{4}\left(\mathrm{cos}\frac{\pi}{\mathrm{9}}+{i}\mathrm{sin}\frac{\pi}{\mathrm{9}}\right)}=\frac{\mathrm{1}}{\mathrm{4}{e}^{\frac{\pi}{\mathrm{9}}{i}} }=\frac{\mathrm{1}}{\mathrm{4}}{e}^{−\frac{\pi}{\mathrm{9}}{i}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{cos}\frac{\pi}{\mathrm{9}}−{i}\mathrm{sin}\frac{\pi}{\mathrm{9}}\right) \\ $$