CAIE P3 2016 June — Question 9

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2016
SessionJune
TopicComplex Numbers Arithmetic
TypeGeometric properties using complex numbers

  1. Sketch this diagram and state fully the geometrical relationship between \(O B\) and \(A C\).
  2. Find, in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real, the complex number \(\frac { u } { v }\).
  3. Prove that angle \(A O B = \frac { 3 } { 4 } \pi\).