8. (a) Sketch, on the Argand diagram below, the locus of points satisfying the equation $$| z - 3 | = 2$$ \includegraphics[max width=\textwidth, alt={}, center]{14f14bf3-88ee-413c-a62d-0914f41a485d-18_1339_1383_370_402}
(b) There is a unique complex number \(w\) that satisfies both $$| w - 3 | = 2 \quad \text { and } \quad \arg ( w + 1 ) = \alpha$$ where \(\alpha\) is a constant such that \(0 < \alpha < \pi\)
(b) (i) Find the value of \(\alpha\).
(b) (ii) Express \(w\) in the form \(r ( \cos \theta + \mathrm { i } \sin \theta )\).
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