a.
Xét $C=\dfrac{1+i}{1+i\sqrt3}$
Ta có:
$C=\dfrac{\sqrt2\left(\cos\dfrac{\pi}{4}+i\sin\dfrac{\pi}{4}\right)}{2\left(\cos\dfrac{\pi}{3}+i\sin\dfrac{\pi}{3}\right)}=\dfrac{1}{\sqrt2}\left(\cos\dfrac{-\pi}{12}+i\sin\dfrac{-\pi}{12}\right)$
Suy ra: $A=C^n=\dfrac{1}{\sqrt{2^n}}\left(\cos\dfrac{-n\pi}{12}+i\sin\dfrac{-n\pi}{12}\right)$