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6 marksComplex Numbers

CAPE Pure Mathematics Unit 2 · May/June 2008 (T&T) · Paper 2 · Question 5(c)(i)

Find the values of h, k \in \mathbb{R} such that 3 + 4\mathrm{i} is a root of the quadratic equation z^2 + hz + k = 0.

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Other parts of this question

  1. 5(a)(i)a)How many 4-digit numbers can be formed if the digits 1, 2, 3, 4, 7, 9 can all be repeated?[2 marks]
  2. 5(a)(i)b)How many 4-digit numbers can be formed if none of the digits 1, 2, 3, 4, 7, 9 can be repeated?[2 marks]
  3. 5(a)(ii)Calculate the probability that a 4-digit number formed without repetition is even.[3 marks]
  4. 5(b)A father and son practise shooting at basketball, and score when the ball hits the basket. The son scores 75\% of the time and the father scores 4 out of…[6 marks]
  5. 5(c)(ii)Use De Moivre's theorem for (\cos \theta + \mathrm{i} \sin \theta)^3 to show that \cos 3\theta = 4\cos^3 \theta - 3\cos \theta.[6 marks]

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