9. (a) Sketch, on the Argand diagram below, the locus of points satisfying the equation
$$| z - 3 | = 2$$
\includegraphics[max width=\textwidth, alt={}, center]{0d8a4ccd-f88a-4f03-a70f-61864d2e30e2-18_1173_1209_301_516}
(b) There is a unique complex number \(w\) that satisfies both
$$| w - 3 | = 2 \text { and } \arg ( w + 1 ) = \alpha$$
where \(\alpha\) is a constant such that \(0 < \alpha < \pi\).
- Find the value of \(\alpha\).
- Express \(w\) in the form \(r ( \cos \theta + i \sin \theta )\).
Give each of \(r\) and \(\theta\) to two significant figures.
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