plumiComplex number arithmetic: OCR MEI A‑Level Further Maths questions
OCR MEI 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.
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All 12 questions on Complex number arithmetic, as a list
- June 2025, Core Pure, Q1 (4 marks): The complex number z satisfies the equation z 2 i z * 1 4 i 0 . + + - = You are given that z x i y , where x and y are real numbers. = + Determine the values of
- 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 2024, AS Core Pure, Q1 (4 marks): + 1 The quadratic equation x ax b 0 , where a and b are real constants, has a root 2 3 i. + = - (a) Write down the other root. [1] (b) Hence or otherwise determ
- 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, Q3 (5 marks): The complex number z satisfies the equation ( z z 5 i ) ( 1 2 i ) *. - = - + Determine z, giving your answer in the form a bi , where a and b are real. [5] +
- November 2020, Core Pure, Q6 (4 marks): - 6 The complex number z satisfies the equation z 4 i z * 11 0 . + = Given that Re z ( ) 2 0 , find z in the form a + bi, where a and b are real numbers. [4]
- 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, Q3 (5 marks): Find real numbers a and b such that ( a b [5] 3 i )( 5 i ) 17 i . - - = -
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