plumiDe Moivre's theorem and roots of unity: WJEC A‑Level Further Maths questions
Every WJEC A-Level Further Maths exam question on 4.1 De Moivre's theorem and roots of unity, 2018–2025, with its mark scheme and examiner’s report.
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All 8 questions on De Moivre's theorem and roots of unity, as a list
- Summer 2025, Unit 4, Q2 (20 marks): 2. (a) Using mathematical induction, prove that n cos isin cos isin n n for positive integer values of n. [7] 4 2 Show that cos4 can be writt
- Summer 2024, Unit 4, Q1 (11 marks): ie r , where 0 2 Express the three cube roots of 5 10i 1. (a) in the form . [6] X ! The three cube roots of 5 10i (b) are plotted in an Argand diagram.
- Summer 2024, Unit 4, Q4 (21 marks): n z 2cos n z cos isin 16cos in the form 4 4. (a) Given that , where , express z n a cos4 b cos2 c , where a, b, c are integers whose val
- Summer 2023, Unit 4, Q3 (9 marks): Given that z = cosθ + isinθ, use de Moivre’s theorem to show that 3. (a) zn + 1 zn = 2cos nθ. [3] Express 32cos6θ in the form acos 6θ + bcos 4θ + ccos 2θ + d, w
- Summer 2023, Unit 4, Q7 (7 marks): Find the cube roots of the complex number z = 11 – 2i, giving your answers in the form x + iy, 7. where x and y are real and correct to three decimal places. [7
- Summer 2022, Unit 4, Q2 (4 marks): − 3 3 i 2. When plotted on an Argand diagram, the four fourth roots of the complex number lie on a circle. Find the equation of this circle. [4]
- Summer 2022, Unit 4, Q9 (12 marks): ( ) 3 Expand cosθ 3 + isinθ 9. (a) (i) . 3 Hence, by using de Moivre’s theorem, show that cosθ can be expressed as (ii) 4cos3 θ 3 − 3cosθ . [6] 3 Hence, or othe
- Summer 2019, Unit 4, Q1 (8 marks): A complex number is defined by z = 3 + 4i. 1. Express z in the form z = reiθ, where –πX θX π. [3] (a) (i) Find the Cartesian coordinates of the vertices of the
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