Question Number 146782 by mathdanisur last updated on 15/Jul/21
$${Find}\:{the}\:{modulus}\:{of}\:{a}\:{complex} \\ $$$${number}: \\ $$$${Z}\:=\:{cos}\:\mathrm{40}\:+\:{i}\:{sin}\:\mathrm{40}\:+\mathrm{1}\:=\:? \\ $$
Answered by Ar Brandon last updated on 15/Jul/21
$$\mathrm{z}=\mathrm{e}^{\mathrm{40i}} +\mathrm{1}=\mathrm{e}^{\mathrm{20i}} \left(\mathrm{e}^{\mathrm{20i}} +\mathrm{e}^{−\mathrm{20i}} \right) \\ $$$$\:\:\:=\mathrm{e}^{\mathrm{20i}} \left(\mathrm{2cos20}\right)\Rightarrow\mid\mathrm{z}\mid=\mathrm{2cos}\left(\mathrm{20}\right) \\ $$
Commented by mathdanisur last updated on 15/Jul/21
$${cool}\:{Ser}\:{thankyou} \\ $$$${how}\:{did}\:{you}\:{change}\:{it}\:{and}\:{write}\:{it} \\ $$$${ase}\:\boldsymbol{{e}}^{\mathrm{40}\boldsymbol{{i}}} .? \\ $$
Commented by Ar Brandon last updated on 16/Jul/21
$$\mathrm{e}^{\mathrm{i}\theta} =\mathrm{cos}\theta+\mathrm{isin}\theta \\ $$
Commented by mathdanisur last updated on 16/Jul/21
$${thanks}\:{Ser} \\ $$