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CAIE A-Level Mathematics A2 3.9.8 Complex Numbers Questions

Practise sketching complex-number loci and regions, then finding extrema of modulus, argument and coordinates.

Syllabus
2028–2030
Course
Mathematics 9709
Level
A2

Exam points

  • sketch loci and shaded regions defined by complex-number conditions
  • find extrema of modulus, argument and real or imaginary parts on regions
  • translate geometric constraints on Argand diagrams into algebraic inequalities

CAIE A-Level Mathematics A2 3.9.8 Complex Numbers Questions question 1

[Maximum number: 6]

Question (a)

(a)

On a single Argand diagram sketch the loci given by the equations |z-3+2 i|=2 and ∣w−3+2i∣=∣w+3−4i∣|w-3+2 \mathrm{i}|=|w+3-4 \mathrm{i}| where z and w are complex numbers.

[ 4 ]

Question (b)

(b)

Hence find the least value of |z-w| for points on these loci. Give your answer in an exact form.

[ 2 ]
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