plumiArgand diagrams, modulus and argument: OCR MEI A‑Level Further Maths questions
OCR MEI 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 13 questions on Argand diagrams, modulus and argument, as a list
- June 2025, Core Pure, Q9 (10 marks): The figure below shows an Argand diagram with a regular pentagon ABCDE. The point A represents the real number 1. The point B represents the complex number w. I
- June 2025, AS Core Pure, Q5 (10 marks): In this question you must show detailed reasoning. + ^ h . The complex number w is given by w – 4 2 4 2 i = (a) (i) Find w . [2] (ii) Find arg w . ( ) [2] The c
- June 2024, Core Pure, Q2 (7 marks): Two complex numbers are given by u =- + and v 1 i =- - . 2 i (a) (i) Find u - in the form a v bi , where a and b are real. [1] + (ii) In this question you must
- June 2023, Core Pure, Q1 (7 marks): (a) The complex number a bi is denoted by z. + (i) Write down z*. [1] (ii) Find Re(iz). [2] 5 i 3 + (b) The complex number w is given by w . = 2 i 3 - (i) In th
- June 2023, AS Core Pure, Q5 (4 marks): The Argand diagram below shows the points representing 1 and z, where z 2 . = Im z Re O 1 Mark the points representing the following complex numbers on the copy
- June 2023, AS Core Pure, Q7 (10 marks): In this question you must show detailed reasoning. The complex number 3 + is denoted by z. i ^ h , express z5 in the form a (a) By expanding i 5 3 bi where a an
- June 2022, AS Core Pure, Q7 (9 marks): On an Argand diagram, the point A represents the complex number z with modulus 2 and 1 1 r The point B represents . argument . z 3 (a) Sketch an Argand diagram
- November 2021, Core Pure, Q3 (6 marks): In this question you must show detailed reasoning. a k. 1 1 The complex numbers z1 and z2 are given by z 2 2i and z 2 cos i sin 1 =- + = r + r 2 6 6 (a) Find th
- November 2021, Core Pure, Q12 (4 marks): Fig. 12 shows a rhombus OACB in an Argand diagram. The points A and B represent the complex numbers z and w respectively. Im C B A O Re Fig. 12 1 Prove that arg
- November 2021, AS Core Pure, Q7 (9 marks): (a) (i) Find the modulus and argument of z1, where z 1 + . i [2] 1 = 1 r (ii) Given that z 2 and arg z ( ) express z2 in a bi form, where a and b are exact , 2
- November 2020, AS Core Pure, Q2 (4 marks): Fig. 2 shows two complex numbers z1 and z2 represented on an Argand diagram. Im z1 z2 Re O Fig. 2 (a) On the copy of Fig. 2 in the Printed Answer Booklet, mark
- November 2020, AS Core Pure, Q3 (7 marks): In this question you must show detailed reasoning. 2 - The roots of the equation x 2 x 4 0 are a and b. + = (a) Find a and b in modulus-argument form. [4] 3 (b)
- June 2018, AS Core Pure, Q9 (9 marks): Fig. 9 shows a sketch of the region OPQ of the Argand diagram defined by % / % /. 1 1 z z z z 4 2 arg | G k | r G G r 4 3 Im Q P Re O Fig. 9 (i) Find, in modulu
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