OCR FP1 2008 January — Question 6

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2008
SessionJanuary
TopicComplex Numbers Argand & Loci

6 The loci \(C _ { 1 }\) and \(C _ { 2 }\) are given by $$| z | = | z - 4 \mathbf { i } | \quad \text { and } \quad \arg z = \frac { 1 } { 6 } \pi$$ respectively.
  1. Sketch, on a single Argand diagram, the loci \(C _ { 1 }\) and \(C _ { 2 }\).
  2. Hence find, in the form \(x +\) i \(y\), the complex number represented by the point of intersection of \(C _ { 1 }\) and \(C _ { 2 }\).