| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2022 |
| Session | January |
| Marks | 7 |
| Topic | Complex Numbers Argand & Loci |
| Type | Intersection of two loci |
| Difficulty | Standard +0.3 This is a straightforward complex numbers question requiring basic skills: calculating modulus/argument (routine), sketching a circle locus (standard), and sketching a half-line locus (standard). All techniques are textbook exercises with no problem-solving or novel insight required. Slightly easier than average due to the direct nature of each part. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02b Express complex numbers: cartesian and modulus-argument forms4.02k Argand diagrams: geometric interpretation4.02o Loci in Argand diagram: circles, half-lines |
2.
The complex number $3 + 4 \mathrm { i }$ is denoted by $a$.\\
(i) Find $| a |$ and $\arg a$.\\
(ii) Sketch on a single Argand diagram the loci given by
\begin{enumerate}[label=(\alph*)]
\item $| z - a | = | a |$,
\item $\quad \arg ( z - 3 ) = \arg a$.\\[0pt]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2022 Q2 [7]}}