plumiLoci and regions in the Argand diagram: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on B.4 Loci and regions in the Argand diagram, 2019–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 10 questions on Loci and regions in the Argand diagram, as a list
- June 2025, AS Paper 1, Q16 (8 marks): A circle C is drawn on an Argand diagram. The roots of the equation w2 + 4w + 9 = 0 lie on C 16 (a) Show that the roots of the equation w2 + 4w + 9 = 0 are –2 +
- June 2024, Paper 2, Q17 (9 marks): The Argand diagram below shows a circle C Re Im – 1 – 1 5 6 7 8 9 10 4 3 2 1 5 6 7 8 4 3 2 1 O 17 (a) Write down the equation of the locus of C in the form │z –
- June 2024, AS Paper 1, Q17 (9 marks): The circle C represents the locus of points satisfying the equation |z – ai| = b where a and b are real constants. The circle C intersects the imaginary axis at
- June 2023, Paper 1, Q2 (1 mark): The diagram below shows a locus on an Argand diagram. 2 Re Im – 3 O Which of the equations below represents the locus shown above? Circle your answer. [1 mark]
- June 2023, Paper 2, Q10 (8 marks): The region R on an Argand diagram satisfies both jz + 2ij × 3 and − p 6 × arg (z) × p 2 10 (a) Sketch R on the Argand diagram below. [3 marks] 1 1 – 1 – 2 – 3 –
- June 2022, Paper 1, Q8 (11 marks): (a) The complex number w is such that arg (w + 2i) = tan−1 1 2 It is given that w = x + iy , where x and y are real and x > 0 Find an equation for y in terms of
- June 2022, AS Paper 1, Q12 (6 marks): (a) Sketch, on the Argand diagram below, the locus of points satisfying the equation jz − 2ij = 2 [2 marks] Re Im O – 1 – 1 – 2 – 3 – 4 – 5 5 4 3 2 1 – 2 – 3 –
- November 2021, Paper 2, Q8 (6 marks): The complex number z satisfies the equations jz× − 1 − 2ij = jz − 3j and jz − aj = 3 where a is real. Show that a must lie in the interval 1 − s t p , 1 + s t p
- November 2020, AS Paper 1, Q18 (5 marks): The locus of points L1 satisfies the equation jzj = 2 The locus of points L2 satisfies the equation arg (z + 4) = p 4 18 (a) Sketch L1 on the Argand diagram bel
- June 2019, Paper 2, Q6 (6 marks): A circle C in the complex plane has equation jz − 2 − 5ij = a The point z1 on C has the least argument of any point on C, and arg (z1) = p 4 Prove that a = 3p2
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