OCR FP1 2016 June — Question 6

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2016
SessionJune
TopicComplex Numbers Argand & Loci

6 In an Argand diagram the points \(A\) and \(B\) represent the complex numbers \(5 + 4 \mathrm { i }\) and \(1 + 2 \mathrm { i }\) respectively.
  1. Given that \(A\) and \(B\) are the ends of a diameter of a circle \(C\), find the equation of \(C\) in complex number form. The perpendicular bisector of \(A B\) is denoted by \(l\).
  2. Sketch \(C\) and \(l\) on a single Argand diagram.
  3. Find the complex numbers represented by the points of intersection of \(C\) and \(l\).