A-level · Complex numbers

Loci in the Argand diagramExam-style questions

Reading a condition on z as a set of points in the Argand diagram: |z − a| = r is a circle centre a radius r, |z − a| = |z − b| is the perpendicular bisector of a and b, and arg(z − a) = θ is a half-line from a. Describing and sketching these loci, turning them into Cartesian equations, and shading the regions given by the matching inequalities.

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16 questions · A Level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 1Level 2Level 3Level 4Level 5
  1. 1
    The complex number zz satisfies ∣z−4−3i∣=2|z - 4 - 3i| = 2.

    Find the least and greatest values of arg⁡z\arg z, giving your answers in radians to 33 decimal places. (5 marks)
    Level 5 · 5 marksTry it
  2. 2
    The region RR in the Argand diagram consists of the points satisfying both

    ∣z∣⩽4and∣z−4∣⩽∣z∣|z| \leqslant 4 \qquad \text{and} \qquad |z - 4| \leqslant |z|
    (a) Describe the two conditions geometrically. (2 marks)
    (b) Find the exact area of RR. (4 marks)
    Level 5 · 6 marksTry it