[填空题]
Let z=r$e^{i\frac{\pi}{3}}$ where r∈R$^+$.
1.For r= $sqrt{2}$,
1.1.express $z^2$ and $z^3$ in the form a+bi where a,b∈R;
$z^2$=-1+$\sqrt{x}$i and $z^3$=-2$\sqrt{2}$+yi; x= ,y= .
1.2.draw $z^2$ and $z^3$ on the following Argand diagram.
2.Given that the integer powers of w=(3−3i)z lie on a unit circle centred at the origin, find the value of r.
r=$\frac{\sqrt{x}}{y}$ ; x= .y= .
