plumiExponential form and de Moivre's theorem: OCR MEI A‑Level Further Maths questions
OCR MEI 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, Core Pure, Q15 (9 marks): ^ ^h h 4 i 4 i 15 (a) Show that i i a b , where a and b are integers to be determined. [2] 3 e 3 e - cos 4 - - = + i The infinite series C and S are defined as
- June 2024, Core Pure, Q13 (10 marks): 1 i 13 The complex number z is defined as z e i where 0 r. = 1 1 i 3 2 On an Argand diagram, the point O represents the complex number 0, and the points P1, P2,
- June 2022, Core Pure, Q11 (8 marks): An Argand diagram with the point A representing a complex number z1 is shown below. Im z1 A Re O 2 r and z e 4 r respectively. i i The complex numbers z2 and z3
- November 2021, Core Pure, Q10 (13 marks): (a) Show on an Argand diagram the points representing the three cube roots of unity. [2] 3 - , expressing them in the form reii, where (b) (i) Find the exact ro
- November 2020, Core Pure, Q11 (8 marks): In this question you must show detailed reasoning. In Fig. 11, the points A, B, C, D, E and F represent the complex sixth roots of 64 on an Argand diagram. The
- June 2019, Core Pure, Q10 (8 marks): In this question you must show detailed reasoning. 3 = (a) You are given that - + is a root of the equation 1 i z a b i , where a and b are real numbers. + Find
- June 2019, Core Pure, Q16 (12 marks): i i 16 (a) Show that ( 2 e i )( 2 e i ) 5 4 cos . [3] - - - = - i Series C and S are defined by 1 1 1 1 C cos cos 2 cos 3 cos n , = i + i + i + f + i 2 4 8 n 2
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