$z_2 =2 (\dfrac{1}{2} +\dfrac{\sqrt 3}{2} i)=2(\cos \dfrac{\pi}{3} +i \sin \dfrac{\pi}{3})$
Khi đó $(z_1 . z_2)^{18} = \bigg (\cos \dfrac{\pi}{12} -i \sin \dfrac{\pi}{12} \bigg )^{18} .2^{18} \bigg (\cos \dfrac{\pi}{3} +i \sin \dfrac{\pi}{3} \bigg )^{18}$
$=2^{18} .\bigg (\cos \dfrac{18\pi}{12} -i \sin \dfrac{18\pi}{12} \bigg ) . \bigg (\cos \dfrac{18\pi}{3} +i \sin \dfrac{18\pi}{3} \bigg )$
$=2^{18} .\bigg (\cos \dfrac{3\pi}{2} -i \sin \dfrac{3\pi}{2} \bigg ) . \bigg (\cos 6\pi +i \sin 6\pi \bigg )=2^{18} .i$