SPS SPS FM 2020 June — Question 11

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2020
SessionJune
TopicComplex Numbers Argand & Loci

11. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0e7cab3d-c1e6-4420-93b4-eca5af704432-10_766_791_283_701} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} The Argand diagram, shown in Figure 1, shows a circle \(C\) and a half-line \(l\).
  1. Write down the equation of the locus of points represented in the complex plane by
    1. the circle \(C\),
    2. the half-line \(l\).
  2. Use set notation to describe the set of points that lie on both \(C\) and \(l\).
  3. Find the complex numbers that lie on both \(C\) and \(l\), giving your answers in the form \(a + \mathrm { i } b\), where \(a , b \in \mathbb { R }\).