Moduli and principal arguments of powers and conjugates

The complex numbers \(z\) and \(w\) satisfy \(|z|=2\), \(\arg z=\dfrac{\pi}{3}\), \(|w|=3\) and \(\arg w=-\dfrac{3\pi}{4}\). Find the exact modulus and principal argument of each of the following, giving arguments in the interval \(-\pi<\theta\leq\pi\). Here \(z^*\) denotes the complex conjugate of \(z\).

1. \(w^3z^2\)[2]
2. \(\dfrac{w^2}{z^5}\)[2]
3. \(z^{-2}w^5\)[2]
4. \(\dfrac{(\mathrm{i}w)^7}{3(z^*)^2}\)[3]
5. \(\dfrac{z^*(1-\mathrm{i})^3}{w}\)[3]