CAIE P3 2023 November — Question 4

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2023
SessionNovember
TopicComplex Numbers Arithmetic
TypeComplex number parameter problems

4 The complex number \(u\) is defined by \(u = \frac { 3 + 2 \mathrm { i } } { a - 5 \mathrm { i } }\), where \(a\) is real.
  1. Express \(u\) in the Cartesian form \(x + \mathrm { i } y\), where \(x\) and \(y\) are in terms of \(a\).
  2. Given that \(\arg u = \frac { 1 } { 4 } \pi\), find the value of \(a\).