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7 marksComplex Numbers

CAPE Pure Mathematics Unit 2 · May/June 2023 · Paper 2 · Question 1(c)

Given that 3z² - pz + 2q = 0 has root 3 - 5i, determine the values of p and q where p, q ∈ R.

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Other parts of this question

  1. 1(a)(i)Sketch the locus of z on the Argand diagram below.[3 marks]
  2. 1(a)(ii)Determine the Cartesian equation of the locus of z.[4 marks]
  3. 1(b)Given that x²y – 2xy² = cos(xy), determine dy/dx.[5 marks]
  4. 1(d)Using DeMoivre's theorem, determine the square root of 1 - i√3, expressing your answer in radians.[6 marks]

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