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3 marksCo-ordinate Geometry

CAPE Pure Mathematics Unit 1 · May/June 2001 · Paper 2 · Question 4(a)(i)

This section covers Module 1.2. Answer both questions. The complex number, z, is expressed in the form x + iy, where x, y ∈ R. Express the complex number, (z-1)/(z+1), in a similar form. The argument of the complex number, (z-1)/(z+1), is π/4.

Find the equation connecting x and y.

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Other parts of this question

  1. 4(a)Express the complex number, (z-1)/(z+1), in a similar form.[7 marks]
  2. 4(a)(ii)Show that the equation represents a circle, C.[3 marks]
  3. 4(a)(iii)Determine the centre and radius of C.[2 marks]
  4. 4(b)(i)Find the values of t such that the vector t r₁ + r₂ is perpendicular to the vector r₂ + r₃.[5 marks]
  5. 4(b)(ii)Find the position vector of C relative to O.[3 marks]
  6. 4(b)(iii)Determine cos AÔC.[2 marks]

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