plumiArgand diagrams, modulus and argument: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on B.3 Argand diagrams, modulus and argument, 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 15 questions on Argand diagrams, modulus and argument, as a list
- June 2025, Paper 1, Q2 (1 mark): The point A on the Argand diagram represents the complex number z The point B is the reflection in the imaginary axis of the point A A B Re Im O Which complex n
- June 2025, Paper 1, Q5 (3 marks): The complex number 1z has argument tan 1 1 5 − The complex number 2z = –2 – 4i Find 1 2 arg z z Give your answer as a number in the range
- June 2025, AS Paper 1, Q6 (4 marks): The complex numbers w and z are defined as follows: w = 2(cos 0.4 + i sin 0.4) and z = 6(cos 1.2 + i sin 1.2) 6 (a) Express z2 in the form r(cos θ + i sin θ) [2
- June 2024, Paper 1, Q10 (6 marks): The complex numbers z and w are defined by z = cos π 4 + i sin π 4 _ and w = cos π 6 + i sin π 6 By evaluating the product zw, show that tan 5π 12 = 2 + √ 3 [6
- 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 2023, Paper 2, Q9 (7 marks): The complex number z is such that z = 1 + i 1 − ki where k is a real number. 9 (a) Find the real part of z and the imaginary part of z, giving your answers in t
- June 2023, AS Paper 1, Q8 (4 marks): Abdoallah wants to write the complex number –1 + i√ 3 in the form r (cos θ + i sin θ) where r ≥ 0 and – π < θ ≤ π Here is his method: r = √ (–1)2 + (√ 3)2 = √ 1
- June 2022, Paper 1, Q2 (1 mark): Simplify cos 6p 13 + i sin 6p 13 cos 2p 13 − i sin 2p 13 Tick (3) one box. [1 mark] cos 8p 13 + i sin 8p 13 cos 8p 13 − i sin 8p 13 cos 4p 13 + i sin 4p 13 cos
- June 2022, AS Paper 1, Q4 (1 mark): The complex numbers w and z are defined as w = 2( cos a + i sin a) z = 3( cos b + i sin b) Find the product wz Tick (3) one box. [1 mark] 5(cos (ab) + i sin (ab
- November 2021, Paper 1, Q6 (10 marks): (a) Show that the equation (2z − z≤)≤ = z2 has exactly four solutions and state these solutions. [7 marks] 6 (b) (i) Plot the four solutions to the equation in
- November 2021, Paper 2, Q2 (1 mark): Find arg (−4 − 7i) to the nearest degree. Circle your answer. [1 mark] −120° −60° 30° 60°
- November 2021, AS Paper 1, Q1 (1 mark): The complex number o is shown below on the Argand diagram. Im ω O Re Which of the following complex numbers could be o? Tick (3) one box. [1 mark] cos (−2) + i
- November 2020, Paper 2, Q2 (1 mark): Given that arg (a + bi) = j , where a and b are positive real numbers and 0 < j < p 2 , three of the following four statements are correct. Which statement is n
- November 2020, AS Paper 1, Q1 (1 mark): Express the complex number 1 − i 3 p in modulus-argument form. Tick (3) one box. [1 mark] 2 cosp 3 + i sinp 3 2 cos 2p 3 + i sin 2p 3 2 cos − p 3 + i sin − p 3
- June 2019, AS Paper 1, Q8 (7 marks): Given that z1 = 2 cosp 6 + i sin p 6 and z2 = 2 cos 3p 4 + i sin 3p 4 8 (a) Find the value of jz1z2j [1 mark] 8 (b) Find the value of arg z1 z2 [1 mark] 8 (c) S
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