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Question Number 176549 by doline last updated on 21/Sep/22

donner la forme trigonometrique de 1/4(cosΠ/9+isinΠ/9)

$${donner}\:{la}\:{forme}\:{trigonometrique}\:{de}\:\mathrm{1}/\mathrm{4}\left({cos}\Pi/\mathrm{9}+{isin}\Pi/\mathrm{9}\right) \\ $$

Answered by Ar Brandon last updated on 21/Sep/22

(1/(4(cos(π/9)+isin(π/9))))=(1/(4e^((π/9)i) ))=(1/4)e^(−(π/9)i)   =(1/4)(cos(π/9)−isin(π/9))

$$\frac{\mathrm{1}}{\mathrm{4}\left(\mathrm{cos}\frac{\pi}{\mathrm{9}}+{i}\mathrm{sin}\frac{\pi}{\mathrm{9}}\right)}=\frac{\mathrm{1}}{\mathrm{4}{e}^{\frac{\pi}{\mathrm{9}}{i}} }=\frac{\mathrm{1}}{\mathrm{4}}{e}^{−\frac{\pi}{\mathrm{9}}{i}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{cos}\frac{\pi}{\mathrm{9}}−{i}\mathrm{sin}\frac{\pi}{\mathrm{9}}\right) \\ $$

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