6. You are given the complex number \(w = 2 + 2 \sqrt { 3 } i\).
- Express \(w\) in modulus-argument form.
- Indicate on an Argand diagram the set of points, \(z\), which satisfy both of the following inequalities.
$$- \frac { \pi } { 2 } \leqslant \arg z \leqslant \frac { \pi } { 3 } \text { and } | z | \leqslant 4$$
Mark \(w\) on your Argand diagram and find the greatest value of \(| z - w |\).
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[9]
(Total 12 marks)
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