(a) First, calculate \(u^2\):

\(u = 2e^{\frac{1}{4} \pi i}\)

\(u^2 = (2e^{\frac{1}{4} \pi i})^2 = 4e^{\frac{1}{2} \pi i}\)

Now, calculate \(\frac{u^2}{w}\):

\(w = 3e^{\frac{1}{3} \pi i}\)

\(\frac{u^2}{w} = \frac{4e^{\frac{1}{2} \pi i}}{3e^{\frac{1}{3} \pi i}} = \frac{4}{3} e^{(\frac{1}{2} \pi i - \frac{1}{3} \pi i)} = \frac{4}{3} e^{\frac{1}{6} \pi i}\)

Thus, \(r = \frac{4}{3}\) and \(\theta = \frac{1}{6} \pi\).

(b) For \(w^n\) to be real and positive, \(n \theta\) must be a multiple of \(2\pi\), where \(\theta = \frac{1}{3} \pi\).

\(n \cdot \frac{1}{3} \pi = 2k\pi\) for some integer \(k\).

\(n = 6k\)

The smallest positive integer \(n\) is \(n = 6\).