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CAIE A-Level Mathematics 3.9.7 Geometry of Complex Operations

Practise interpreting conjugation, addition, subtraction, multiplication and division geometrically as reflections, translations, rotations and enlargements on an Argand diagram.

Syllabus
2028–2030
Course
Mathematics 9709
Level
A2

Exam points

  • describe conjugation as reflection in the real axis and reverse the argument sign
  • interpret multiplication or division by reⁱθ as an enlargement and directed rotation
  • use complex differences as directed segments to prove parallelism or length relationships

3.9.7—Complex numbers question 1

[Maximum number: 2]

The complex numbers u and v are defined by u=-4+2 i and v=3+i.

In an Argand diagram, with origin O, the points A, B and C represent the complex numbers u, v and 2 u+v respectively.

State fully the geometrical relationship between O A and B C.

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