plumiExponential form and de Moivre's theorem: OCR A‑Level Further Maths questions
OCR A-Level Further Maths past-paper questions on 2.5 Exponential form and de Moivre's theorem, 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 7 questions on Exponential form and de Moivre's theorem, as a list
- June 2025, Pure Core 1, Q8 (7 marks): In this question you must show detailed reasoning. In this question, arguments of complex numbers are in the interval [ 0 2r . , ) (a) Given that z 5 5i , expre
- June 2024, Pure Core 2, Q2 (6 marks): In this question you must show detailed reasoning. 2 - (a) Solve the equation x 6 x 58 0 . Give your solutions in the form a + bi where a and b are + = real num
- 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
- 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 1, Q5 (5 marks): J N 3 1 3 i KK 2 OO where ei 5 By expanding z , z i show that , 4 cos 2 cos 6 3 cos 2 [5] . + = = i + i 2 z L P
- November 2020, Pure Core 1, Q9 (9 marks): 2 9 You are given that the cubic equation 2 x px qx 3 0 , where p and q are real numbers, has a + + - = complex root 1 i 2 . a = + (a) Write down a second compl
- 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
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