[tex]\displaystyle\bf\\z_1=2\left(cos\frac{\pi}{6}+i\,sin\frac{\pi}{6}\right)\\\\z_1=2\left(\frac{\sqrt{3}}{2}+\frac{1}{2}i\right)\\\\\boxed{\bf z_1=\sqrt{3}+i}\\\\z_2=\frac{4}{\sqrt{3}+i}\\\\z_2=\frac{4(\sqrt{3}-i)}{(\sqrt{3}+i)(\sqrt{3}-i)}\\\\z_2=\frac{4(\sqrt{3}-i)}{3-i^2} \\\\z_2=\frac{4(\sqrt{3}-i)}{3-(-1)}\\\\z_2=\frac{4(\sqrt{3}-i)}{4}\\\\\boxed{\bf z_2=\sqrt{3}-i}\\\\\\z_1+z_2=\sqrt{3}+i+\sqrt{3}-i\\\\z_1+z_2=\sqrt{3}+\sqrt{3}+i-i\\\\\boxed{\bf z_1+z_2=2\sqrt{3} \in R}[/tex]
