[问答题]
Let $z=r e^{1 \frac{4}{3}} where r \in \mathbb{R}^{+}$ .
1. For $r=\sqrt{2}$ ,
1. express $z^{2}$ and $z^{3}$ in the form $+b \mathrm{i}$ where $a, b \in \mathbb{R}$ ;
2. draw $z^{2}$ and $z^{3}$ on the following Argand diagram.
$\text { 2. Given that the integer powers of } w=(3-3 \mathrm{i}) z \text { lie on a unit circle centred at the origin, find the value of } r \text {. }$
