- (i) The point \(P\) is one vertex of a regular pentagon in an Argand diagram.
The centre of the pentagon is at the origin.
Given that \(P\) represents the complex number \(6 + 6 \mathrm { i }\), determine the complex numbers that represent the other vertices of the pentagon, giving your answers in the form \(r \mathrm { e } ^ { \mathrm { i } \theta }\)
(ii) (a) On a single Argand diagram, shade the region, \(R\), that satisfies both
$$| z - 2 i | \leqslant 2 \quad \text { and } \quad \frac { 1 } { 4 } \pi \leqslant \arg z \leqslant \frac { 1 } { 3 } \pi$$
(b) Determine the exact area of \(R\), giving your answer in simplest form.