[填空题]
Let z=r$e^{i\frac{\pi}{3}}$ where r∈R$^+$.
1.For r= $sqrt{3}$,
1.1.express $z^2$ and $z^3$ in the form a+bi where a,b∈R;
$z^2$=$\frac{3}{2}$+$\frac{3\sqrt{x}}{y}$i and $z^3$=0+$3sqrt{z}$i; x= ,y= ,z= .
1.2.draw $z^2$ and $z^3$ on the following Argand diagram.
2.Given that the integer powers of w=$\frac{z}{6+2i}$ lie on a unit circle centred at the origin, find the value of r.
r=$x\sqrt{y}$ ; x= .y= .
