plumiComplex numbers: Edexcel International A Level Further Maths questions
Every Edexcel International A Level Further Maths exam question on FP1.1 Complex numbers, 2019–2025, with its mark scheme and examiner’s report.
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All 20 questions on Complex numbers, as a list
- June 2025, Further Pure 1 (FP1), Q5 (8 marks): The complex number z1 is given by 1 7 7 cos isin 6 6 π π z r where r is a positive constant. The complex number z2 has modulus 5 Given that | z1z2 | = 1
- June 2025, Further Pure 1 (FP1), Q7 (10 marks): f (z) = Pz 4 – 36z 3 + Qz 2 + 192z + 68 where P and Q are real constants. Given that 3 + 5i is a root of the equation f (z) = 0 (a) write down another root of t
- January 2025, Further Pure 1 (FP1), Q4 (8 marks): f(z) = 6 3 2 z Az Bz C + + + where A, B and C are integers. Given that z 2 3 17 3 i is a root of the equation f(z) = 0 (a) write down the other complex root of
- June 2024, Further Pure 1 (FP1), Q2 (9 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. f(z) = z z z p p 3 2 13 59
- June 2024, Further Pure 1 (FP1), Q4 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The complex number z is defin
- January 2024, Further Pure 1 (FP1), Q2 (9 marks): f(z) = 2z 3 + pz 2 + qz – 41 where p and q are integers. The complex number 5 – 4i is a root of the equation f(z) = 0 (a) Write down another complex root of thi
- January 2024, Further Pure 1 (FP1), Q9 (6 marks): Given that 3 1 5i 2 4i z λ λ where λ is a real constant, (a) determine z, giving your answer in the form x + yi, where x and y are real and in terms of λ. Given
- June 2023, Further Pure 1 (FP1), Q2 (7 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Given that x = 2 + 3i is a root of the
- June 2023, Further Pure 1 (FP1), Q6 (10 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. z1 = 3 + 2i z2 = 2 + 3i z3 =
- January 2023, Further Pure 1 (FP1), Q3 (10 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. f ( )z z pz z 4 24 108 3 2 wh
- June 2022, Further Pure 1 (FP1), Q1 (6 marks): z1 = 3 + 3i z2 = p + qi p, q ∈ Given that ½z1z2 ½ = 15 2 (a) determine ½z2 ½ Given also that p = –4 (b) determine the possible values of q (c) Show z1 and the
- June 2022, Further Pure 1 (FP1), Q4 (8 marks): f(z) = 2z4 – 19z3 + Az2 + Bz – 156 where A and B are constants. The complex number 5 – i is a root of the equation f(z) = 0 (a) Write down another complex root
- January 2022, Further Pure 1 (FP1), Q2 (8 marks): The complex numbers z1 and z2 are given by z1 = 3 + 5i and z2 = –2 + 6i (a) Show z1 and z2 on a single Argand diagram. (b) Without using your calculator and sho
- January 2022, Further Pure 1 (FP1), Q4 (8 marks): The equation x 4 + Ax 3 + Bx 2 + Cx + 225 = 0 where A, B and C are real constants, has • a complex root 4 + 3i • a repeated positive real root (a) Write down th
- October 2021, Further Pure 1 (FP1), Q4 (7 marks): f(z) = 2z 3 – z 2 + az + b where a and b are integers. The complex number –1 – 3i is a root of the equation f(z) = 0 (a) Write down another complex root of this
- June 2021, Further Pure 1 (FP1), Q2 (7 marks): The complex numbers z1, z2 and z3 are given by z1 = 2 − i z2 = p − i z3 = p + i where p is a real number. (a) Find z z z 2 3 1 in the form a + bi where a and b
- June 2021, Further Pure 1 (FP1), Q5 (7 marks): f ( ) ( ) ( ) x x d x x d = + − + + ( ) 9 8 10 1 2 2 where d is a positive constant. (a) Find the four roots of f ( x ) giving your answers in terms of d. Given
- January 2021, Further Pure 1 (FP1), Q2 (5 marks): Given that x = + 3 8 71 8 i is a root of the equation 4x3 − 19x2 + px + q = 0 (a) write down the other complex root of the equation. Given that x = 4 is also a
- January 2021, Further Pure 1 (FP1), Q6 (11 marks): The complex number z is defined by z = – λ + 3i where λ is a positive real constant Given that the modulus of z is 5 (a) write down the value of λ (b) determine
- October 2020, Further Pure 1 (FP1), Q3 (9 marks): f(z) = z4 + az3 + bz2 + cz + d where a, b, c and d are integers. The complex numbers 3 + i and –1 – 2i are roots of the equation f(z) = 0 (a) Write down the oth
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