2016 TPJC P2 Q4 (a)

The complex number \(w\) is given by \(3+3\left( \sqrt{3} \right)\mathbf{i}\).

1. Find the modulus and argument of \(w\) , giving your answers in exact form.
2. Without using a calculator, find the smallest positive integer value of \(n\) for which \({{\left( \frac{{{w}^{3}}}{{{w}^{*}}} \right)}^{n}}\) is a real number.