OCR FP1 2014 June — Question 7

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2014
SessionJune
TopicComplex Numbers Argand & Loci

7 The loci \(C _ { 1 }\) and \(C _ { 2 }\) are given by \(\arg ( z - 2 - 2 \mathrm { i } ) = \frac { 1 } { 4 } \pi\) and \(| z | = | z - 10 |\) 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 $$0 \leqslant \arg ( z - 2 - 2 \mathrm { i } ) \leqslant \frac { 1 } { 4 } \pi \text { and } | z | \geqslant | z - 10 | .$$