pluminth roots and roots of unity: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on B.6 nth roots and roots of unity, 2019–2025, 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 5 questions on nth roots and roots of unity, as a list
- June 2025, Paper 2, Q9 (9 marks): (a) It is given that, for the complex number z, = + 1 1 z z Find ( ) Re z [3 marks] 9 (b) Show that the only solutions of the equation = + 3 1 1 w w
- June 2023, Paper 2, Q6 (5 marks): (a) Express −5 − 5i in the form reiy, where −p < y × p [2 marks] 6 (b) The point on an Argand diagram that represents −5 − 5i is one of the vertices of an equil
- June 2022, Paper 1, Q12 (17 marks): The Argand diagram shows the solutions to the equation z5 = 1 Im Re z5 z2 z3 z4 z1 12 (a) Solve the equation z5 = 1 giving your answers in the form z = cosy + i
- November 2020, Paper 1, Q6 (9 marks): Let w be the root of the equation z7 = 1 that has the smallest argument a in the interval 0 < a < p 6 (a) Prove that wn is also a root of the equation z7 = 1 fo
- June 2019, Paper 1, Q9 (9 marks): (a) Solve the equation z3 = 2 p − 6 p i , giving your answers in the form reiy where r > 0 and 0 × y < 2p [5 marks] 9 (b) The transformation represented by the
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