Complex number arithmetic: OCR A‑Level Further Maths questions

OCR A-Level Further Maths past-paper questions on 2.1 Complex number arithmetic, 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.

All 18 questions on Complex number arithmetic, as a list

June 2025, Pure Core 2, Q5 (6 marks): In this question you must show detailed reasoning. (a) Use an algebraic method to determine the two square roots of 3 ( 4 7 )i . - + Give your answers in the fo
June 2025, AS Pure Core, Q1 (8 marks): (a) The complex number z is such that z arg z 7 and ( ) 2 2 . radians. = = Express z in cartesian form. [3] + ^ h . (b) Use an algebraic method to determine the
June 2025, AS Pure Core, Q9 (8 marks): z 2 9 (a) Prove that if z is any complex number then ( *) z z [1] . = (b) Prove that if w and z are any complex numbers then ( wz w z [2] ) * * * . = The comple
June 2024, Pure Core 2, Q2 (6 marks): In this question you must show detailed reasoning. 2 - (a) Solve the equation x 6 x 58 0 . Give your solutions in the form a + bi where a and b are + = real num
June 2024, AS Pure Core, Q2 (4 marks): In this question you must show detailed reasoning. 8 i + in the form a (a) Express 2 bi where a and b are real. [2] + i - 2 - (b) Solve the equation x 4 8 x 5 0
June 2023, Pure Core 2, Q2 (7 marks): In this question you must show detailed reasoning. (a) Write the complex number 24 7i in modulus-argument form. [3] - + (b) Solve the simultaneous equations giv
June 2023, AS Pure Core, Q3 (8 marks): In this question you must show detailed reasoning. In this question the principal argument of a complex number lies in the interval [ , 0 2r . ) Complex numbers
June 2023, AS Pure Core, Q8 (9 marks): (a) Solve the equation - . [4] 2 7 i 3 * i ~ + + = ~ (b) Prove algebraically that, for non-zero z, z z * if and only if z is purely imaginary. [2] =- (c) The co
June 2022, Pure Core 1, Q3 (11 marks): In this question you must show detailed reasoning. 2 - (a) Find the roots of the equation z 2 2 z 5 0 . [2] + = The loci C1 and C2 are given by z z 2 i and z 2
June 2022, AS Pure Core, Q5 (7 marks): In this question you must show detailed reasoning. (a) Use an algebraic method to find the square roots of -16 + 30i. [5] 99 5i - + (b) By finding the cube of o
November 2021, Pure Core 2, Q2 (8 marks): In this question you must show detailed reasoning. The complex numbers z1 and z2 are given by z 3 7i and z 2 4i . 1 = - 2 = + (a) Express each of the following
November 2021, AS Pure Core, Q6 (6 marks): In this question you must show detailed reasoning. 2 - (a) Solve the equation z 2 10 z 25 0 giving your answers in the form a bi . [2] + = + (b) Solve the equat
November 2020, Pure Core 2, Q1 (5 marks): In this question you must show detailed reasoning. 2 - Solve the equation z 4 20 z 169 0 . Give your answers in modulus-argument form. [5] + =
November 2020, AS Pure Core, Q1 (6 marks): In this question you must show detailed reasoning. Use an algebraic method to find the square roots of -77 - 36i. [6]
November 2020, AS Pure Core, Q3 (12 marks): In this question you must show detailed reasoning. The complex number 7 - 4i is denoted by z. (a) Giving your answers in the form a + bi, where a and b are rati
June 2019, Pure Core 2, Q7 (7 marks): In an Argand diagram the points representing the numbers 2 + 3i and 1 - i are two adjacent vertices of a square, S. (a) Find the area of S. [3] (b) Find all the
June 2018, AS Pure Core, Q3 (9 marks): In this question you must show detailed reasoning. The complex numbers z1 and z2 are given by z and z a where a is a real number. 2 3i 4i 1 = - 2 = + (i) Expres
June 2018, AS Pure Core, Q5 (10 marks): In this question you must show detailed reasoning. 3i 3 (i) Express ( 2 ) in the form a + ib. [3] + 3 2 (ii) Hence verify that 2 3i is a root of the equation z

Questions, mark schemes and examiner’s reports are © OCR, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? OCR A-Level Further Maths past papers.

The Plumi iPad app also offers exam-style questions with AI feedback on your handwritten working.

648 questions