plumiComplex number arithmetic: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on B.1 Complex number arithmetic, 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 16 questions on Complex number arithmetic, as a list
- June 2025, Paper 1, Q1 (1 mark): The equation + + = 2 4 0 x x c has non-real roots. Find the range of possible values of c Circle your answer. [1 mark] < 4 c ≤4 c ≥4 c > 4 c
- June 2025, Paper 2, Q5 (2 marks): The complex number ( )( ) i i = + + 3 4 5 z c , where c is an integer. It is given that ( ) = Re 7 z Find the value of c [2 marks]
- June 2025, AS Paper 1, Q1 (1 mark): Calculate the product (3 + i)(2 – i) Circle your answer. [1 mark] 5 – i 5 + i 7 – i 7 + i
- 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 1, Q7 (5 marks): The complex numbers z and w satisfy the simultaneous equations _ z + w* = 5 _ 3z* – w = 6 + 4i Find z and w [5 marks]
- 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, AS Paper 1, Q8 (7 marks): (a) The complex number z is given by z = x + iy where x, y ∈ ℝ 8 (a) (i) Write down the complex conjugate z* in terms of x and y [1 mark] ����������������������
- June 2024, AS Paper 1, Q11 (3 marks): The matrices A and B are given by A = 3i –2 a –i and B = 4 5 –2i –1 where a is a real number. Calculate the product AB in terms of a Give your answer in its sim
- 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, Q12 (13 marks): (a) Show that (1 + i)൯ = – 4 [3 marks] 12 (b) The function f is defined by f (z) = z4 + 3z2 – 6z + 10 z ℂ 12 (b) (i) Show that (1 + i) is a root of f (z) = 0 [2
- June 2022, Paper 2, Q1 (1 mark): Find the imaginary part of 5 + i 1 − i Circle your answer. [1 mark] −3 −2 2 3
- June 2022, AS Paper 1, Q5 (3 marks): Show that (2 + i)3 is 2 + 11i [3 marks]
- 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, AS Paper 1, Q10 (8 marks): Matrix A is given by A = 3 i − 1 i 2 10 (a) Show that det A = a + i where a is an integer to be determined. [2 marks] 10 (b) Matrix B is given by B = 14 − 2i b
- June 2019, Paper 1, Q4 (4 marks): Solve the equation 2z − 5iz* = 12 [4 marks]
- June 2019, Paper 2, Q1 (1 mark): Given that z is a complex number, and that z* is the complex conjugate of z, which of the following statements is not always true? Circle your answer. [1 mark]
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