CAIE P3 2003 November — Question 7

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2003
SessionNovember
TopicComplex Numbers Argand & Loci

7 The complex number \(u\) is given by \(u = \frac { 7 + 4 \mathrm { i } } { 3 - 2 \mathrm { i } }\).
  1. Express \(u\) in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real.
  2. Sketch an Argand diagram showing the point representing the complex number \(u\). Show on the same diagram the locus of the complex number \(z\) such that \(| z - u | = 2\).
  3. Find the greatest value of \(\arg z\) for points on this locus.