Solve the equation \(z ^ { 4 } = 2 ( 1 + \mathrm { i } \sqrt { 3 } )\), giving the roots exactly in the form \(r ( \cos \theta + \mathrm { i } \sin \theta )\), where \(r > 0\) and \(0 \leqslant \theta < 2 \pi\).
Sketch an Argand diagram to show the lines from the origin to the point representing \(2 ( 1 + i \sqrt { 3 } )\) and from the origin to the points which represent the roots of the equation in part (i).