Could someone please help me write $z= \frac{(2+2i)^3}{(1+i\sqrt{3})^4}$ on polar form? Could someone please help me write $z = \dfrac{(2+2i)^3}{(1+i\sqrt{3})^4}$  on polar form?
$|z|=\sqrt{2}$
But how do I proceed to get the argument? 
$\mathrm{arg⁡}(z)=\mathrm{arg⁡}(2+2i)^3 - \mathrm{arg⁡}(1+i\sqrt{3})^4$
Thanks /David

Hints: Use $\arctan 1=\frac{1}{4}\pi $ and $\arctan \sqrt{3}=\frac{1}{3}\pi $ in
$$\arg \left( \left( 2+2i\right) ^{3}\right) =3\arg \left( 2+2i\right)
=3 \arctan \frac{2}{2}=3\times \frac{1}{4}\pi $$
and
$$\arg \left( (1+i\sqrt{3})^{4}\right) =4\arg (1+i\sqrt{3})=4\arctan  \frac{\sqrt{3}}{1}=4\times \frac{1}{3}\pi .$$
