OCR FP1 2007 June — Question 8

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2007
SessionJune
TopicComplex Numbers Argand & Loci

8 The loci \(C _ { 1 }\) and \(C _ { 2 }\) are given by \(| z - 3 | = 3\) and arg \(( z - 1 ) = \frac { 1 } { 4 } \pi\) respectively.
  1. Sketch, on a single Argand diagram, the loci \(C _ { 1 }\) and \(C _ { 2 }\).
  2. Indicate, by shading, the region of the Argand diagram for which $$| z - 3 | \leqslant 3 \text { and } 0 \leqslant \arg ( z - 1 ) \leqslant \frac { 1 } { 4 } \pi$$