CAIE A-Level Mathematics 3.9.7 Geometry of Complex Operations

CAIE A-Level Mathematics 3.9.7 Geometry of Complex Operations
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

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

How this is tested

  • 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

Question 3(b)

[Maximum number: 2]

The complex numbers s and t are given by

s=5(cos⁡0.25+isin⁡0.25) and t=6e3is=5(\cos 0.25+\mathrm{i} \sin 0.25) \quad \text { and } \quad t=6 \mathrm{e}^{3 \mathrm{i}}

In an Argand diagram with origin O, the points A and B represent the complex numbers s and st\frac{s}{t} respectively.

By considering the line segments OA and OB, or otherwise, state the two geometric effects of dividing a complex number by 6e3i6e^{3i}.