Moderate -0.8 Part (a) is direct recall of a standard locus (circle with center 2, radius 2). Part (b) requires converting from modulus-argument form to Cartesian form, which is a routine A-level technique involving basic trigonometry. Both parts are straightforward applications of fundamental complex number concepts with no problem-solving required.
3. (a) Sketch on the Argand diagram below the locus of points satisfying the equation \(| z - 2 | = 2\).
\includegraphics[max width=\textwidth, alt={}, center]{ace492d8-1dd0-401e-af74-505ca19d5e9c-08_1260_1303_260_468}
(b) Given that \(| z - 2 | = 2\) and \(\arg ( z - 2 ) = - \frac { \pi } { 3 }\), express \(z\) in the form \(a + b i\) where \(a , b \in \mathbb { R }\). [0pt]
3. (a) Sketch on the Argand diagram below the locus of points satisfying the equation $| z - 2 | = 2$.\\
\includegraphics[max width=\textwidth, alt={}, center]{ace492d8-1dd0-401e-af74-505ca19d5e9c-08_1260_1303_260_468}\\
(b) Given that $| z - 2 | = 2$ and $\arg ( z - 2 ) = - \frac { \pi } { 3 }$, express $z$ in the form $a + b i$ where $a , b \in \mathbb { R }$.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM Pure 2024 Q3 [5]}}