Tìm phần thực a của số phức z = (1-tan(pi/7)/(1 + i.tan(pi/7)))

* Hướng dẫn giải

Đáp án D

$$\begin{gathered} \mathrm{z}=\frac{1-\mathrm{i}.\tan {\displaystyle \frac{\mathrm{\pi }}{7}}}{1+\mathrm{i}.\tan {\displaystyle \frac{\mathrm{\pi }}{7}}}=\frac{\left(1-\mathrm{i}.\tan \frac{\mathrm{\pi }}{7}\right)\left(1-\mathrm{i}.\tan \frac{\mathrm{\pi }}{7}\right)}{1-{\mathrm{i}}^2.{\tan }^2{\displaystyle \frac{\mathrm{\pi }}{7}}} \\ =\frac{1-{\tan }^2{\displaystyle \frac{\mathrm{\pi }}{7}}-2\mathrm{i}.\tan {\displaystyle \frac{\mathrm{\pi }}{7}}}{1+{\tan }^2{\displaystyle \frac{\mathrm{\pi }}{7}}} \\ \Rightarrow \mathrm{Phần} \mathrm{thực} \mathrm{của} \mathrm{số} \mathrm{phức} \mathrm{z} \mathrm{là}: \\ \mathrm{a}=\frac{1-{\tan }^2{\displaystyle \frac{\mathrm{\pi }}{7}}}{1+{\tan }^2\frac{\mathrm{\pi }}{7}} =\frac{{\cos }^2{\displaystyle \frac{\mathrm{\pi }}{7}}-{\sin }^2{\displaystyle \frac{\mathrm{\pi }}{7}}}{{\cos }^2{\displaystyle \frac{\mathrm{\pi }}{7}}+{\sin }^2{\displaystyle \frac{\mathrm{\pi }}{7}}} \\ =\cos \frac{2\mathrm{\pi }}{7} \end{gathered}$$