(iv) Given ∣z∣=11|z|=11∣z∣=11 and arg(z)=−11π12\arg(z)=-\dfrac{11\pi}{12}arg(z)=−1211π. z=11(cos(−11π12)+isin(−11π12))z=11\left(\cos\left(-\frac{11\pi}{12}\right)+i\sin\left(-\frac{11\pi}{12}\right)\right)z=11(cos(−1211π)+isin(−1211π)) cos(−11π12)=−6+24,sin(−11π12)=−6−24\cos\left(-\frac{11\pi}{12}\right)=-\frac{\sqrt{6}+\sqrt{2}}{4},\quad \sin\left(-\frac{11\pi}{12}\right)=-\frac{\sqrt{6}-\sqrt{2}}{4}cos(−1211π)=−46+2,sin(−1211π)=−46−2 z=−11(6+2)4−11(6−2)4i\boxed{z=-\frac{11(\sqrt{6}+\sqrt{2})}{4}-\frac{11(\sqrt{6}-\sqrt{2})}{4}i}z=−411(6+2)−411(6−2)i