Số phức nào dưới đây có mođun khác 1? 1 + cos(pi/7)

* Hướng dẫn giải

Đáp án A

$$\begin{gathered} \mathrm{Xét} \mathrm{đáp} \mathrm{án} \mathrm{A}: \\ \mathrm{z}=1+\cos \frac{\mathrm{\pi }}{7}+\mathrm{i}.\sin \frac{\mathrm{\pi }}{7} \\ \Rightarrow \left|\mathrm{z}\right|={\left(1+\cos \frac{\mathrm{\pi }}{7}\right)}^2+{\left(\sin \frac{\mathrm{\pi }}{7}\right)}^2=1+2\cos \frac{\mathrm{\pi }}{7}+{\left(\cos \frac{\mathrm{\pi }}{7}\right)}^2+{\left(\sin \frac{\mathrm{\pi }}{7}\right)}^2 \\ =2+2\cos \frac{\mathrm{\pi }}{7}\ne 1 \\ \Rightarrow \mathrm{Đáp} \mathrm{án} \mathrm{A} \mathrm{đúng} \\ \mathrm{Xét} \mathrm{đáp} \mathrm{án} \mathrm{B}: \\ \mathrm{z}=\cos \frac{2000\mathrm{\pi }}{3}+\mathrm{i}.\sin \frac{2000\mathrm{\pi }}{3} \\ \Rightarrow \left|\mathrm{z}\right|=\sqrt{{\left(\cos \frac{2000\mathrm{\pi }}{3}\right)}^2+{\left(\sin \frac{2000\mathrm{\pi }}{3}\right)}^2}=1 \Rightarrow \mathrm{Đáp} \mathrm{án} \mathrm{B} \mathrm{loại} \\ \mathrm{Xét} \mathrm{đáp} \mathrm{án} \mathrm{C}: \\ \mathrm{z}=\frac{1-2\mathrm{i}\sqrt{2}}{3} \\ \Rightarrow \left|\mathrm{z}\right|=\sqrt{{\left(\frac{1}{3}\right)}^2+{\left(\frac{-2\sqrt{2}}{3}\right)}^2}=\sqrt{\frac{1}{9}+\frac{8}{9}}=1 \Rightarrow \mathrm{Đáp} \mathrm{án} \mathrm{C} \mathrm{loại} \\ \mathrm{Xét} \mathrm{đáp} \mathrm{án} \mathrm{D}: \\ \mathrm{z}=\frac{4-\mathrm{i}}{4+\mathrm{i}}=\frac{15}{17}+\frac{8}{17}\mathrm{i} \\ \Rightarrow \left|\mathrm{z}\right|=\sqrt{{\left(\frac{15}{17}\right)}^2+{\left(\frac{8}{17}\right)}^2}=\sqrt{\frac{289}{289}}=1 \Rightarrow \mathrm{Đáp} \mathrm{án} \mathrm{D} \mathrm{loại} \end{gathered}$$