Complex numbers: past paper questions
Real questions on complex numbers
The newest 20 of 41 written questions. Open one to see it on the real paper.
- 9231/21 · October/November 2025 · Q8b[6]
6-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · October/November 2025 · Q4a[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · October/November 2025 · Q8b[6]
6-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · October/November 2025 · Q8c[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · October/November 2025 · Q8d[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · May/June 2025 · Q3[6]
6-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · May/June 2025 · Q1[5]
5-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · May/June 2025 · Q3[6]
6-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · May/June 2025 · Q5a[6]
6-mark “Use” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · May/June 2025 · Q5b[4]
4-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · October/November 2024 · Q8a[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/13 · May/June 2024 · Q2c[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · May/June 2024 · Q4b[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · May/June 2024 · Q1[5]
5-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · May/June 2024 · Q6a[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/23 · May/June 2024 · Q6b[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · October/November 2023 · Q3a[4]
4-mark “Use” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · May/June 2023 · Q3a[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · May/June 2023 · Q3a[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/22 · October/November 2022 · Q5a[1]
1-mark “Write” question — its maths and diagrams are best seen on the paper.
See it on the paper →
What examiners said
After expanding ( cos θ + i sin θ ) using the binomial expansion, most candidates grouped together terms contributing to the real part before applying the identity cos2 θ + sin2 θ = 1 to fully justify the given result. Alternatively, a few candidates worked from the right-hand side to the left-hand side, applying 2cosθ = z + z −1 , and were usually successful too.
— Examiner report, October/November 2023, 9231/22 Q3(a) (Cambridge)
After expanding ( cosθ + i sinθ ) using the binomial expansion, most candidates grouped together terms contributing to the real part before applying the identity cos2 θ + sin2 θ = 1 to fully justify the given result. Alternatively, a few candidates worked from the right-hand side to the left-hand side, applying 2cosθ = z + z −1 , and were usually successful too.
— Examiner report, October/November 2022, 9231/22 Q5(b) (Cambridge)
While it was common to see Ae = λe written, only the strongest candidates gave a correct algebraic argument by multiplying both sides of the equation by A −1 on the left-hand side.
— Examiner report, October/November 2022, 9231/22 Q7(a) (Cambridge)
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