Edexcel F2 2024 June — Question 9

Exam BoardEdexcel
ModuleF2 (Further Pure Mathematics 2)
Year2024
SessionJune
TopicComplex numbers 2

  1. In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
  1. Use De Moivre's theorem to show that $$\cos 6 \theta \equiv 32 \cos ^ { 6 } \theta - 48 \cos ^ { 4 } \theta + 18 \cos ^ { 2 } \theta - 1$$
  2. Hence determine the smallest positive root of the equation $$48 x ^ { 6 } - 72 x ^ { 4 } + 27 x ^ { 2 } - 1 = 0$$ giving your answer to 3 decimal places.