OCR FP1 2012 June — Question 7

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2012
SessionJune
TopicComplex Numbers Argand & Loci

7 The loci \(C _ { 1 }\) and \(C _ { 2 }\) are given by \(| z - 3 - 4 \mathrm { i } | = 4\) and \(| z | = | z - 8 \mathrm { i } |\) respectively.
  1. Sketch, on a single Argand diagram, the loci \(C _ { 1 }\) and \(C _ { 2 }\).
  2. Hence find the complex numbers represented by the points of intersection of \(C _ { 1 }\) and \(C _ { 2 }\).
  3. Indicate, by shading, the region of the Argand diagram for which $$| z - 3 - 4 i | \leqslant 4 \text { and } | z | \geqslant | z - 8 i | .$$