Complex numbers: past paper questions
Real questions on complex numbers
The newest 20 of 82 written questions. Open one to see it on the real paper.
- 9709/32 · May/June 2026 · Q3a[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · May/June 2026 · Q3b[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · May/June 2026 · Q4[5]
5-mark “Give” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · October/November 2025 · Q3a[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · October/November 2025 · Q3b[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/33 · October/November 2025 · Q4[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/33 · October/November 2025 · Q7[6]
6-mark “Give” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · May/June 2025 · Q3[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · May/June 2025 · Q5[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/33 · May/June 2025 · Q4a[3]
3-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/33 · May/June 2025 · Q4b[3]
3-mark “State” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/33 · May/June 2025 · Q6[6]
6-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/31 · October/November 2024 · Q8a[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/31 · October/November 2024 · Q8b[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/31 · October/November 2024 · Q8c[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/31 · October/November 2024 · Q8d[1]
1-mark “Use” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · October/November 2024 · Q3[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · October/November 2024 · Q5a[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/32 · October/November 2024 · Q5b[2]
2-mark “Describe” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9709/33 · October/November 2024 · Q1a[2]
2-mark question — its maths and diagrams are best seen on the paper.
See it on the paper →
What examiners said
This question was done reasonably well. However, an appreciable number of candidates seemed to be very unconfident with this topic and it was not uncommon to see no attempt at a diagram. In drawing an Argand diagram candidates should use a ruler and pencil, and they are also welcome to use other geometric equipment. They should also use a reasonable scale so that the diagram is not ridiculously sm...
— Examiner report, October/November 2023, 9709/33 Q2 (Cambridge)
Starting from the quadratic factor it is straightforward to demonstrate the given result. Substituting z = −1 + 2 6i into the cubic equation and simplifying was more complicated. Using z = −1 + 2 6i and its conjugate to form the quadratic factor was simpler, but few candidates tried this. Candidates who used their calculators to write down the three roots of the cubic had not demonstrated that any...
— Examiner report, May/June 2023, 9709/31 Q10(b) (Cambridge)
Very few candidates recognised that the earlier parts of the question had been leading them to the roots of this equation. The first mark, for stating that the square roots of –3 were solutions of the equation, should have been accessible to all. Most of the candidates who made any attempt at all started by squaring −1 + 2 6i and made no useful progress. The majority of candidates offered no respo...
— Examiner report, May/June 2023, 9709/31 Q10(c) (Cambridge)
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