pluminth roots and roots of unity: OCR A‑Level Further Maths questions
OCR A-Level Further Maths past-paper questions on 2.6 nth roots and roots of unity, 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 6 questions on nth roots and roots of unity, as a list
- June 2024, Pure Core 2, Q9 (12 marks): In this question, the argument of a complex number is defined as being in the range [0, 2r). ~ , where k = 0, 1, 2, ..., n - 1, are the n nth roots of unity for
- June 2023, Pure Core 1, Q3 (5 marks): 3 i r . - + 5 i 3 (a) Show that 3e [2] = 6 2 ^ h, giving the roots in the 9 3 3 i - + 5 = (b) Hence determine the exact roots of the equation z 2 form reiiwhere
- June 2022, Pure Core 1, Q9 (5 marks): The cube roots of unity are represented on the Argand diagram below by the points A, B and C. Im(z) B L O M A Re(z) N C The points L, M and N are the midpoints
- November 2020, Pure Core 1, Q4 (4 marks): In this question you must show detailed reasoning. (a) Determine the square roots of 25i in the form reii, where 0 1 2 r . [3] G i (b) Illustrate the number 25i
- November 2020, Pure Core 2, Q8 (9 marks): In this question you must show detailed reasoning. The complex number 4 i 48 is denoted by z. - + (a) Determine the cube roots of z, giving the roots in exponen
- June 2019, Pure Core 1, Q9 (12 marks): In this question you must show detailed reasoning. 5 = 2 2 You are given the complex number cos i sin and the equation z 1 . ~ = r + r 5 5 (a) Show that ~ is a
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