OCR FP1 2015 June — Question 5

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2015
SessionJune
TopicComplex Numbers Argand & Loci

5 The loci \(C _ { 1 }\) and \(C _ { 2 }\) are given by \(| z + 2 | = 2\) and \(\arg ( z + 2 ) = \frac { 5 } { 6 } \pi\) respectively.
  1. Sketch, on a single Argand diagram, the loci \(C _ { 1 }\) and \(C _ { 2 }\).
  2. Find the complex number represented by the intersection of \(C _ { 1 }\) and \(C _ { 2 }\).
  3. Indicate, by shading, the region of the Argand diagram for which $$| z + 2 | \leqslant 2 \text { and } \frac { 5 } { 6 } \pi \leqslant \arg ( z + 2 ) \leqslant \pi .$$