| Exam Board | SPS |
|---|---|
| Module | SPS ASFM (SPS ASFM) |
| Year | 2020 |
| Session | May |
| Marks | 5 |
| Topic | Complex Numbers Argand & Loci |
| Type | Modulus-argument form conversion |
| Difficulty | Easy -1.3 This question tests basic complex number definitions (modulus, argument, conjugate) and geometric interpretation. Part (a) requires only direct application of formulas with no problem-solving, while part (b) asks for standard knowledge that conjugates are reflections in the real axis. This is routine recall with minimal computational challenge, significantly easier than average A-level questions. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02k Argand diagrams: geometric interpretation |
You are given that $z = 3 - 4\mathrm{i}$.
\begin{enumerate}[label=(\alph*)]
\item Find
\begin{itemize}
\item $|z|$,
\item $\arg(z)$,
\item $z^*$.
\end{itemize}
[3]
On an Argand diagram the complex number $w$ is represented by the point $A$ and $w^*$ is represented by the point $B$.
\item Describe the geometrical relationship between the points $A$ and $B$. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS ASFM 2020 Q1 [5]}}