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8 marksAlgebraic Operations

CAPE Pure Mathematics Unit 1 · May/June 2004 · Paper 2 · Question 4(a)

A complex number, z, is expressed in the form x + iy, where x, y ∈ R.

Express the complex number, w = (z-1)/(z+2), in a similar form.

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Other parts of this question

  1. 4(b)(i)Find the equation connecting x and y in the form ax² + by² + cx + dy + f = 0 where a, b, c, d, f are integers.[4 marks]
  2. 4(b)(ii)Show that the equation in (i) represents a circle, C.[3 marks]
  3. 4(b)(iii)Determine the centre and radius of the circle C.[4 marks]
  4. 4(c)Find the position vector of P.[6 marks]

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