(iii) Given ∣z∣=7|z|=7∣z∣=7 and arg(z)=23π12\arg(z)=\dfrac{23\pi}{12}arg(z)=1223π. z=7(cos23π12+isin23π12)z=7\left(\cos\frac{23\pi}{12}+i\sin\frac{23\pi}{12}\right)z=7(cos1223π+isin1223π) 23π12=2π−π12\frac{23\pi}{12}=2\pi-\frac{\pi}{12}1223π=2π−12π cos23π12=6+24,sin23π12=−6−24\cos\frac{23\pi}{12}=\frac{\sqrt{6}+\sqrt{2}}{4},\quad \sin\frac{23\pi}{12}=-\frac{\sqrt{6}-\sqrt{2}}{4}cos1223π=46+2,sin1223π=−46−2 z=7(6+2)4−7(6−2)4i\boxed{z=\frac{7(\sqrt{6}+\sqrt{2})}{4}-\frac{7(\sqrt{6}-\sqrt{2})}{4}i}z=47(6+2)−47(6−2)i