Cho số phức $\Large z=1 \cdot \cos \frac{\pi}{8}+i \cdot \sin \frac{\p

Cho số phức $\Large z=1 \cdot \cos \frac{\pi}{8}+i \cdot \sin \frac{\pi}{8}$. Tính $\Large z^{1012}$

• A. $\Large \left(2 \sin \dfrac{\pi}{16}\right)^{2012}\left(\dfrac{\sqrt{2}}{2}+\dfrac{\sqrt{2}}{2} i \right)$
• B. $\Large \left(2 \sin \dfrac{\pi}{8}\right)^{2012}\left(\dfrac{\sqrt{2}}{2}+\dfrac{\sqrt{2}}{2} i \right)$
• C. $\Large \left(2 \sin \dfrac{\pi}{16}\right)^{2012}\left(\dfrac{1}{2}+\dfrac{\sqrt{3}}{2} i \right)$
• D. $\Large \left(2 \sin \dfrac{\pi}{16}\right)^{2012}\left(\dfrac{\sqrt{3}}{2}+\dfrac{1}{2} i \right)$

Ta có 

$\Large \begin{array}{l}
z=2 \sin ^{2} \dfrac{\pi}{16}+2 i \sin \dfrac{\pi}{16} \cos \dfrac{\pi}{16} \\
=2 \sin \dfrac{\pi}{16}\left(\sin \dfrac{\pi}{16}+i \cos \dfrac{\pi}{16}\right) \\
=2 \sin \dfrac{\pi}{16}\left(\cos \dfrac{7 \pi}{16}+i \sin \dfrac{7 \pi}{16}\right) \\
\Rightarrow z^{2012}
\end{array}$
$\Large \begin{array}{l}
=\left(2 \sin \dfrac{\pi}{16}\right)^{2012}\left(\cos \dfrac{7 \pi}{16}+i \sin \dfrac{7 \pi}{16}\right)^{2012} \\
=\left(2 \sin \dfrac{\pi}{16}\right)^{2012}\left(\cos \dfrac{3521 \pi}{4}+i \sin \dfrac{3521 \pi}{4}\right) \\
=\left(2 \sin \dfrac{\pi}{16}\right)^{2012}\left(\cos \dfrac{\pi}{4}+i \sin \dfrac{\pi}{4}\right) \\
=\left(2 \sin \dfrac{\pi}{16}\right)^{2012}\left(\dfrac{\sqrt{2}}{2}+\dfrac{\sqrt{2}}{2} i \right)
\end{array}$
Chọn A