Question Number 198232 by SANOGO last updated on 14/Oct/23
$${find}\: \\ $$$${Im}\left(\underset{{k}={o}} {\overset{{n}} {\sum}}{sin}\left({k}\right)\right) \\ $$
Answered by witcher3 last updated on 14/Oct/23
$$\mathrm{sin}\left(\mathrm{k}\right)\in\mathbb{R} \\ $$$$\mathrm{Im}\left(\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{sin}\left(\mathrm{k}\right)\right)=\mathrm{Im}\left(\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{sin}\left(\mathrm{k}\right)+\mathrm{i}.\mathrm{0}\right)=\mathrm{0} \\ $$