Aloha :)
$$z_1=4\,e^{-i\frac\pi6}=4\cdot\left(\cos\frac\pi6-i\,\sin\frac\pi6\right)=4\cdot\left(\frac{\sqrt3}{2}-i\,\frac12\right)=2\sqrt3-2\,i$$$$z_2=2\,e^{i\frac{16\pi}{3}}=2\cdot\left(\cos\frac{16\pi}{3}+i\,\sin\frac{16\pi}{3}\right)=2\cdot\left(-\frac12+i\cdot\left(-\frac{\sqrt3}{2}\right)\right)=-1-\sqrt3\,i$$
$$z_3=\red{-3}\green{-3}i=\sqrt{(\red{-3})^2+(\green{-3})^2}\;e^{\green-i\,\arccos\left(\frac{\red{-3}}{\sqrt{(\red{-3})^2+(\green{-3})^2}}\right)}=\sqrt{18}\,e^{-i\,\frac{3\pi}{4}}$$$$z_4=\red{2}\green{+\sqrt{12}}i=\sqrt{\red2^2+(\green{\sqrt12})^2}\;e^{\green+i\,\arccos\left(\frac{\red2}{\sqrt{\red2^2+(\green{\sqrt12})^2}}\right)}=4\,e^{i\,\frac{\pi}{3}}$$
