OCR MEI FP1 2009 June — Question 8

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2009
SessionJune
TopicComplex Numbers Argand & Loci

8 Fig. 8 shows an Argand diagram. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{fa71f270-53cb-44ba-b3a6-3953fa5c4232-3_421_586_1105_778} \captionsetup{labelformat=empty} \caption{Fig. 8}
\end{figure}
  1. Write down the equation of the locus represented by the perimeter of the circle in the Argand diagram.
  2. Write down the equation of the locus represented by the half-line \(\ell\) in the Argand diagram.
  3. Express the complex number represented by the point P in the form \(a + b \mathrm { j }\), giving the exact values of \(a\) and \(b\).
  4. Use inequalities to describe the set of points that fall within the shaded region (excluding its boundaries) in the Argand diagram.