OCR FP1 AS 2017 December — Question 2

Exam BoardOCR
ModuleFP1 AS (Further Pure 1 AS)
Year2017
SessionDecember
TopicComplex Numbers Argand & Loci

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