AQA Further AS Paper 1 2024 June — Question 8

Exam BoardAQA
ModuleFurther AS Paper 1 (Further AS Paper 1)
Year2024
SessionJune
TopicComplex Numbers Arithmetic
TypeLinear equations in z and z*
8
  1. The complex number \(z\) is given by \(z = x + i y\) where \(x , y \in \mathbb { R }\) 8
    1. Write down the complex conjugate \(z ^ { * }\) in terms of \(x\) and \(y\) 8
  3. (ii) Hence prove that \(z z ^ { * }\) is real for all \(z \in \mathbb { C }\)
    8
  4. The complex number \(w\) satisfies the equation $$3 w + 10 \mathrm { i } = 2 w ^ { \star } + 5$$ 8
    1. Find \(w\)
      8
  6. (ii) Calculate the value of \(w ^ { 2 } \left( w ^ { * } \right) ^ { 2 }\)
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