Edexcel CP2 Specimen — Question 4

Exam BoardEdexcel
ModuleCP2 (Core Pure 2)
SessionSpecimen
TopicComplex Numbers Arithmetic
TypeComplex conjugate properties and proofs
  1. A complex number \(z\) has modulus 1 and argument \(\theta\).
    1. Show that
    $$z ^ { n } + \frac { 1 } { z ^ { n } } = 2 \cos n \theta , \quad n \in \mathbb { Z } ^ { + }$$
  2. Hence, show that $$\cos ^ { 4 } \theta = \frac { 1 } { 8 } ( \cos 4 \theta + 4 \cos 2 \theta + 3 )$$
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