Edexcel CP1 2024 June — Question 1

Exam BoardEdexcel
ModuleCP1 (Core Pure 1)
Year2024
SessionJune
TopicComplex Numbers Arithmetic
TypeGiven two complex roots, find all roots

1. $$\mathrm { f } ( z ) = z ^ { 4 } - 6 z ^ { 3 } + a z ^ { 2 } + b z + 145$$ where \(a\) and \(b\) are real constants.
Given that \(2 + 5 \mathrm { i }\) is a root of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\)
  1. determine the other roots of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\)
  2. Show all the roots of \(\mathrm { f } ( \mathrm { z } ) = 0\) on a single Argand diagram.