plumiArgand diagrams, modulus and argument: OCR A‑Level Further Maths questions
OCR 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.
All papers
All years
Loading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDF
All 13 questions on Argand diagrams, modulus and argument, as a list
- June 2025, Pure Core 1, Q8 (7 marks): In this question you must show detailed reasoning. In this question, arguments of complex numbers are in the interval [ 0 2r . , ) (a) Given that z 5 5i , expre
- 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 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 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
- 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 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, 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 2019, AS Pure Core, Q1 (5 marks): You are given that z 3 4 i . = - (a) Find • z , • arg z , ( ) • z*. [3] On an Argand diagram the complex number w is represented by the point A and w* is repres
- 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
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.