CAIE P3 2023 November — Question 8

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

8 It is given that \(\frac { 2 + 3 a \mathrm { i } } { a + 2 \mathrm { i } } = \lambda ( 2 - \mathrm { i } )\), where \(a\) and \(\lambda\) are real constants.
  1. Show that \(3 a ^ { 2 } + 4 a - 4 = 0\).
  2. Hence find the possible values of \(a\) and the corresponding values of \(\lambda\).