(a) Without using a calculator, use the formula for the solution of a quadratic equation to solve \((2 - i)z^2 + 2z + 2 + i = 0\). Give your answers in the form \(a + bi\).

(b) The complex number \(w\) is defined by \(w = 2e^{\frac{1}{4}\pi i}\). In an Argand diagram, the points \(A, B\) and \(C\) represent the complex numbers \(w, w^3\) and \(w^*\) respectively (where \(w^*\) denotes the complex conjugate of \(w\)). Draw the Argand diagram showing the points \(A, B\) and \(C\), and calculate the area of triangle \(ABC\).