plumiArgand diagrams, modulus and argument: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 2.3 Argand diagrams, modulus and argument, 2018–2025, 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 Argand diagrams, modulus and argument, as a list
- June 2025, Core Pure 1, Q6 (5 marks): f (z) = z3 + az2 + bz + c where a, b and c are real constants The roots of the equation f (z) = 0 are z1, z2 and z3 When plotted on an Argand diagram, the point
- June 2025, Core Pure 2, Q1 (6 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Given that z 2 2 3i and w 1 3
- June 2025, AS Core Pure, Q1 (6 marks): z = 3 – 3i (a) Write z in the form r(cos θ + i sin θ) where –π < θ π (2) (b) Show and label on a single Argand diagram (i) the point P representing z (ii) the
- June 2023, Core Pure 1, Q3 (10 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. z1 = –4 + 4i (a) Express z1 in the for
- June 2023, AS Core Pure, Q4 (8 marks): (i) (a) Show that 2 3 5 1 i i i k( ) where k is a constant to be determined. (Solutions relying on calculator technology are not acceptable.) (3) Given that • n
- June 2022, Core Pure 2, Q1 (3 marks): A student was asked to answer the following: For the complex numbers z1 = 3 – 3i and z2 = 3 + i , find the value of arg z z 1 2 The student’s attempt
- June 2022, AS Core Pure, Q2 (10 marks): (a) Express the complex number w = 4 3 − 4i in the form r (cos θ + i sin θ) where r > 0 and −π < θ π (4) (b) Show, on a single Argand diagram, (i) the point r
- November 2021, Core Pure 2, Q1 (5 marks): Given that 1 2 3 cos isin 3 3 2 cos isin 12 12 π π z π π z = + = − (a) write down the ex
- November 2020, AS Core Pure, Q2 (8 marks): Given that 1 1 2 1 2 2 3i 39 2 arg( ) 4 = + = = z z z π z z where z1 and z2 are complex numbers, (a) write z1 in the form r(cos θ + i sin θ) Give the exact valu
- June 2019, Core Pure 2, Q6 (9 marks): In an Argand diagram, the points A, B and C are the vertices of an equilateral triangle with its centre at the origin. The point A represents the complex number
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