OCR FP1 2009 June — Question 6

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2009
SessionJune
TopicComplex Numbers Argand & Loci

6 The complex number \(3 - 3 \mathrm { i }\) is denoted by \(a\).
  1. Find \(| a |\) and \(\arg a\).
  2. Sketch on a single Argand diagram the loci given by
    (a) \(| z - a | = 3 \sqrt { 2 }\),
    (b) \(\quad \arg ( z - a ) = \frac { 1 } { 4 } \pi\).
  3. Indicate, by shading, the region of the Argand diagram for which $$| z - a | \geqslant 3 \sqrt { 2 } \quad \text { and } \quad 0 \leqslant \arg ( z - a ) \leqslant \frac { 1 } { 4 } \pi$$