[问答题]
Let $z=r e^{\mathrm{i} \frac{\pi}{6}}$ where $r \in \mathbb{R}^{+}$ .
1. For $r=\sqrt{3}$ ,
1. express $z^{2}$ and $z^{3}$ in the form $a+b \mathrm{i}$ where $a, b \in \mathbb{R}$ ;
2. draw $z^{2}$ and $z^{3}$ on the following Argand diagram.
2. Given that the integer powers of $w=\frac{z}{6+2 \mathrm{i}}$ lie on a unit circle centred at the origin, find the value of r .
