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5 marksComplex Numbers

CAPE Pure Mathematics Unit 2 · May/June 2022 · Paper 2 · Question 1(c)

A complex number, z, is such that arg(z-2) = π/2 and arg(z) = π/3. Determine the complex number z.

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Other parts of this question

  1. 1(a)Using DeMoivre's theorem, prove that sin 5θ / sin θ = 5 - 20 sin² θ + 16 sin⁴ θ.[7 marks]
  2. 1(b)Given that 3 + 5i is a root of the quadratic equation z² + pz + q = 0, determine the values of p, q ∈ R.[7 marks]
  3. 1(d)Given that (x² + y²)³ = ax²y, use implicit differentiation to determine dy/dx.[6 marks]

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