OCR MEI Further Pure Core AS 2020 November — Question 2

Exam BoardOCR MEI
ModuleFurther Pure Core AS (Further Pure Core AS)
Year2020
SessionNovember
TopicComplex Numbers Argand & Loci

2 Fig. 2 shows two complex numbers \(z _ { 1 }\) and \(z _ { 2 }\) represented on an Argand diagram. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{55a4a9f1-ed86-44bb-8759-dfee0b66f56d-2_985_997_781_239} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure}
  1. On the copy of Fig. 2 in the Printed Answer Booklet, mark points representing each of the following complex numbers.
    • \(\mathrm { Z } _ { 1 } { } ^ { * }\)
    • \(z _ { 2 } - z _ { 1 }\)
    • In this question you must show detailed reasoning.
    In the case where \(z _ { 1 } = 1 + 2 \mathrm { i }\) and \(z _ { 2 } = 3 + \mathrm { i }\), find \(\frac { z _ { 2 } - z _ { 1 } } { z _ { 1 } ^ { * } }\) in the form \(a + \mathrm { i } b\), where \(a\) and \(b\) are real numbers.