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4 marksComplex Numbers

CAPE Pure Mathematics Unit 2 · May/June 2026 · Paper 2 · Question 1(a)

This section covers complex numbers. Express a given complex number in the form x + yi.

Express the complex number 5-3i / 4+2i in the form x + yi where x and y are real numbers.

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Other parts of this question

  1. 1(b)(i)a)Calculate the EXACT value of |z|.[2 marks]
  2. 1(b)(i)b)Calculate the EXACT value of arg z.[2 marks]
  3. 1(b)(ii)Hence, use de Moivre's theorem to determine the value of z^12.[4 marks]
  4. 1(c)Determine an expression for dy/dx in terms of x and y.[6 marks]
  5. 1(d)Show that y = -x + π/2 is the tangent to the curve y = ln(1 + sin 2x) at the point where x = π/2.[7 marks]

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