Edexcel CP1 2019 June — Question 1

Exam BoardEdexcel
ModuleCP1 (Core Pure 1)
Year2019
SessionJune
TopicComplex Numbers Arithmetic
TypeGiven two complex roots, find all roots

1. $$f ( z ) = z ^ { 4 } + a z ^ { 3 } + b z ^ { 2 } + c z + d$$ where \(a , b , c\) and \(d\) are real constants.
Given that \(- 1 + 2 \mathrm { i }\) and \(3 - \mathrm { i }\) are two roots of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\)
  1. show all the roots of \(f ( z ) = 0\) on a single Argand diagram,
  2. find the values of \(a , b , c\) and \(d\).