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3 marksComplex Numbers

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

A point z moves in the complex plane such that |z - 2 - 3i| = |4 - 2i - z|.

Sketch the locus of z on the Argand diagram below.

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Other parts of this question

  1. 1(a)(ii)Determine the Cartesian equation of the locus of z.[4 marks]
  2. 1(b)Given that x²y – 2xy² = cos(xy), determine dy/dx.[5 marks]
  3. 1(c)Given that 3z² - pz + 2q = 0 has root 3 - 5i, determine the values of p and q where p, q ∈ R.[7 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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