OCR MEI Further Pure Core AS 2020 November — Question 3

Exam BoardOCR MEI
ModuleFurther Pure Core AS (Further Pure Core AS)
Year2020
SessionNovember
TopicComplex Numbers Argand & Loci

3 In this question you must show detailed reasoning.
The roots of the equation \(x ^ { 2 } - 2 x + 4 = 0\) are \(\alpha\) and \(\beta\).
  1. Find \(\alpha\) and \(\beta\) in modulus-argument form.
  2. Hence or otherwise show that \(\alpha\) and \(\beta\) are both roots of \(x ^ { 3 } + \lambda = 0\), where \(\lambda\) is a real constant to be determined.