8 Given that \(z _ { 1 } = 2 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)\) and \(z _ { 2 } = 2 \left( \cos \frac { 3 \pi } { 4 } + i \sin \frac { 3 \pi } { 4 } \right)\)
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- Find the value of \(\left| z _ { 1 } z _ { 2 } \right|\)
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- Find the value of \(\arg \left( \frac { z _ { 1 } } { z _ { 2 } } \right)\)
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- Sketch \(z _ { 1 }\) and \(z _ { 2 }\) on the Argand diagram below, labelling the points as \(P\) and \(Q\) respectively.
[0pt]
[2 marks]
\includegraphics[max width=\textwidth, alt={}, center]{948391d8-10ad-44ce-b254-7f1aaac5c82c-10_764_869_1546_587}
8 - A third complex number \(w\) satisfies both \(| w | = 2\) and \(- \pi < \arg w < 0\)
Given that \(w\) is represented on the Argand diagram as the point \(R\), find the angle \(P \widehat { R } Q\).
Fully justify your answer.