Edexcel FP1 2016 June — Question 4

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2016
SessionJune
TopicComplex Numbers Arithmetic
TypeQuadratic from one complex root

4. $$z = \frac { 4 } { 1 + \mathrm { i } }$$ Find, in the form \(a + \mathrm { i } b\) where \(a , b \in \mathbb { R }\)
  1. \(Z\)
  2. \(z ^ { 2 }\) Given that \(z\) is a complex root of the quadratic equation \(x ^ { 2 } + p x + q = 0\), where \(p\) and \(q\) are real integers,
  3. find the value of \(p\) and the value of \(q\).