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5 marksComplex Numbers

CAPE Pure Mathematics Unit 2 · May/June 2009 · Paper 2 · Question 5(c)(ii)

Hence, or otherwise, solve for z the equation z^2 - (3 + 2\mathrm{i})z + (5 + \mathrm{i}) = 0.

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  1. 5(a)A committee of 4 persons is to be chosen from 8 persons, including Mr Smith and his wife. Mr Smith will not join the committee without his wife, but his wife…[5 marks]
  2. 5(b)(i)the numbers on BOTH balls are even[4 marks]
  3. 5(b)(ii)the number on one ball is odd and the number on the other ball is even.[4 marks]
  4. 5(c)(i)Find complex numbers u = x + \mathrm{i}y such that x and y are real numbers and u^2 = -15 + 8\mathrm{i}.[7 marks]

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