(a) Given the complex numbers \(u = a + ib\) and \(w = c + id\), where \(a, b, c\) and \(d\) are real, prove that \((u + w)^* = u^* + w^*\).

(b) Solve the equation \((z + 2 + i)^* + (2 + i)z = 0\), giving your answer in the form \(x + iy\) where \(x\) and \(y\) are real.