8. (a) Solve the equation \(z ^ { 3 } = \sqrt { 2 } - \sqrt { 6 } \mathrm { i }\), giving your answers in the form \(r \mathrm { e } ^ { \mathrm { i } \theta }\) where \(r > 0\) and \(0 \leq \theta < 2 \pi\)
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(b) The transformation represented by the matrix \(\mathbf { M } = \left[ \begin{array} { l l } 5 & 1
1 & 3 \end{array} \right]\) acts on the points on an Argand Diagram which represent the roots of the equation in part (a). Find the exact area of the shape formed by joining the transformed points.
[0pt] [BLANK PAGE]