Proving Trigonometric Ratios by Complex Numbers Q3

The complex number \(w\) has modulus \(\sqrt{2}\) and argument \(-\frac{3\pi}{4}\), and the complex number \(z\) has modulus \(2\) and argument \(-\frac{\pi}{3}\). Find the exact values of the modulus and argument of \(wz\). By first expressing \(w\) and \(z\) in the form \(x+y\mathrm{i}\), find the exact real and imaginary part of \(wz\). Hence show that \(\sin \frac{\pi}{12}=\frac{\sqrt{3}-1}{2\sqrt{2}}\).