(a)[5]
Without a calculator, use the quadratic formula to solve $(2 - i)z^2 + 2z + 2 + i = 0$. Write the solutions in the form $a + bi$.
(b)[5]
The complex number $w$ is given by $w = 2e^{\frac{1}{4}\pi i}$. On an Argand diagram, points $A$, $B$ and $C$ correspond to $w$, $w^3$ and $w^*$ respectively (where $w^*$ denotes the complex conjugate of $w$). Draw the Argand diagram showing points $A$, $B$ and $C$, and calculate the area of triangle ABC.