# Topic Questions: • understand the idea of a complex number, recall the meaning of the terms real part, imaginary part, modulus, argument, conjugate, and use the fact that two complex numbers are equal if and only if both real and imaginary parts are equal — 9709 P3 Complex numbers > 32 9709 P3 Complex numbers topic questions (109 marks) on understand the idea of a complex number, recall… — 25 papers, 2020–2026. Open the exact question… - Canonical HTML: https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/understand-the-idea-of-a-complex-number-recall-the-meaning-of-the-terms-real-part/ - Markdown mirror: https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/understand-the-idea-of-a-complex-number-recall-the-meaning-of-the-terms-real-part/index.md --- CIE IAL · Mathematics · 9709 P3 · Complex numbers 32 9709 P3 Complex numbers topic questions are tagged to this syllabus point across 25 papers (2020–2026). Only the parts whose knowledge graph matches this syllabus statement are counted, and the table shows which parts of each question are involved. - 32 topic questions - 25 papers - 109 tagged marks - 21.1% of topic questions - 22.2% of topic marks - 2020–2026 - Syllabus 2020–2027 - [All 9709 P3 Complex numbers topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/) - [All paper codes](https://www.examsci.com/topics/) Core finding **This Complex numbers syllabus point appears in 25 9709 P3 papers across 2020–2026, contributing 32 topic questions and 109 marks.** The most recent appearance is 9709/32 March 2026. That equals 21.1% of the 152 topic questions and 22.2% of the 491 marks tagged to Complex numbers. Only parts tagged to this subtopic are counted, so a four-part question can contribute one item and one part's marks. The table lists every matching question, its tagged parts and marks, with a link back to the paper page. Sessions are newest first, so the statement can be traced back through the full paper history. ## Topic questions by session Newest sessions first. Parts and marks count only the parts tagged to this subtopic; “x of y parts” shows how much of the question is tagged elsewhere. Select the paper cell to open the matching question on the paper page, or use **Go to Practice Hub** to answer that exact question in the Interactive Practice Hub. | Paper | Question | Type | Parts | Marks | Difficulty | Practice | | --- | --- | --- | --- | --- | --- | --- | | [**9709/32** March 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2026-march-9709-32/#q-5) | **Q5** Argument and Modulus of Complex Expression - CIE P3 2026 Mar Q5 | FRQ | 2 parts ((a), (b)) | 6 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0fd758f5-8815-4e29-a05d-65b87156efed&question_id=dd680029-3310-426f-bca3-583e3d2a03b2&source_detail=9709%2F32+March+2026) | | [**9709/31** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-october-november-9709-31/#q-5) | **Q5** Argand Diagram Loci and Argument Optimization - CIE Pure Mathematics 2025 Nov Q5 | FRQ | 1 of 2 parts ((b)) | 3 of 6 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=7ffa0858-5cbd-490e-9150-de28164f7cda&question_id=c47eb0b3-83f4-4254-9237-f0c08f6c3957&source_detail=9709%2F31+October%2FNovember+2025) | | [**9709/32** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-october-november-9709-32/#q-3) | **Q3** Complex Numbers Argand Region and Max Argument - CIE A Level Maths 2025 Winter P32 Q3 | FRQ | 2 parts ((a), (b)) | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d271f67a-f544-4649-81c5-cdf7c8a90ccc&question_id=f866e7a0-ae4c-489b-a62f-47a7c8536628&source_detail=9709%2F32+October%2FNovember+2025) | | [**9709/33** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-october-november-9709-33/#q-7) | **Q7** Complex Equations with Conjugate - CIE Pure Mathematics 2025 Nov Paper 33 Q7 | FRQ | 1 part | 6 | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=17e7e425-f366-4dd8-9a85-08207772196f&question_id=8f1dda01-f947-45b0-87d2-dd814d639305&source_detail=9709%2F33+October%2FNovember+2025) | | [**9709/35** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-october-november-9709-35/#q-5) | **Q5** Complex Equation with Conjugate - CIE A Level Mathematics 2025 Winter Paper 35 Q5 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2b303406-630f-44c2-814e-7e47fa277f61&question_id=0b4f982f-6302-4a6c-82f3-373fc8d26ae5&source_detail=9709%2F35+October%2FNovember+2025) | | [**9709/33** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-may-june-9709-33/#q-4) | **Q4** Complex Conjugate Properties - CIE A-Level Math 2025 Jun Paper 33 Q4 | FRQ | 1 of 2 parts ((a)) | 3 of 6 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b947d72f-ec97-4d00-ae14-757145ba0aa9&question_id=c6bfb591-5541-4a34-a6cb-1a890693281b&source_detail=9709%2F33+May%2FJune+2025) | | [**9709/33** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-may-june-9709-33/#q-6) | **Q6** Complex Number Loci and Solutions - CIE A-Level Math 2025 Jun Paper 33 Q6 | FRQ | 1 part | 6 | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b947d72f-ec97-4d00-ae14-757145ba0aa9&question_id=ee31e898-ce9a-44b7-ab7a-281d3142c92a&source_detail=9709%2F33+May%2FJune+2025) | | [**9709/32** March 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-march-9709-32/#q-3) | **Q3** Complex Loci in Argand Diagram - CIE A-Level Math 2025 Mar Paper 32 Q3 | FRQ | 1 of 2 parts ((b)) | 3 of 6 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ebe23b18-f2b2-4e16-8e60-c5ac5649cb15&question_id=1f12d905-30f7-488b-b48a-65779c5223ac&source_detail=9709%2F32+March+2025) | | [**9709/31** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-october-november-9709-31/#q-8) | **Q8** Complex Number Inversion and Loci - CIE A-Level Maths 2024 Nov Paper 31 Q8 | FRQ | 1 of 4 parts ((b)) | 3 of 9 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=70a34762-5adb-4bbc-a073-ccdcbf562e7c&question_id=bc1d91a3-534c-4541-92e7-196a7817dfa8&source_detail=9709%2F31+October%2FNovember+2024) | | [**9709/33** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-october-november-9709-33/#q-4) | **Q4** Solving Complex Number Equation - CIE A-Level Pure Mathematics 2024 Nov Q4 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=eea0ef07-a2e6-40ec-b1f1-0940ce02a199&question_id=ce94be5a-2e94-448a-84f6-569d8a0925e6&source_detail=9709%2F33+October%2FNovember+2024) | | [**9709/31** May/June 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-may-june-9709-31/#q-4) | **Q4** Polar and Exponential Form of Complex Numbers - CIE A-Level Maths 2024 Jun Paper 31 Q4 | FRQ | 1 of 2 parts ((a)) | 2 of 4 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d001bb3e-de7a-4991-8014-a2761a618aba&question_id=e029c70b-c849-40c5-953f-a6949d726555&source_detail=9709%2F31+May%2FJune+2024) | | [**9709/33** May/June 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-may-june-9709-33/#q-3) | **Q3** Square Roots of Complex Number - CIE A-Level Pure Mathematics | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=7e0feb6b-4f09-4f55-8eeb-a9c09d82ec52&question_id=281fc327-8d57-4830-83fc-42355a336d14&source_detail=9709%2F33+May%2FJune+2024) | | [**9709/32** March 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-march-9709-32/#q-3) | **Q3** Exponential Form of Complex Numbers - CIE 9709 March 2024 Paper 32 Q3 | FRQ | 1 of 2 parts ((a)) | 3 of 6 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=e042eca9-7da3-4a8b-b612-449ce3e020fd&question_id=285ae85e-7864-4a83-8335-6ad04862321f&source_detail=9709%2F32+March+2024) | | [**9709/32** October/November 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2023-october-november-9709-32/#q-8) | **Q8** Complex Equality with Real Constants - CIE 9709 2023 Nov Paper 32 Q8 | FRQ | 2 parts ((a), (b)) | 7 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=3fb73dde-04cc-4e60-91c5-1ddfee06f24d&question_id=f00b37f8-cbe4-41f5-9164-f5f087d1bd90&source_detail=9709%2F32+October%2FNovember+2023) | | [**9709/32** May/June 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2023-may-june-9709-32/#q-5) | **Q5** Complex Polynomial Evaluation and Argument - CIE Pure Mathematics 2023 Q5 | FRQ | 1 of 2 parts ((b)) | 3 of 6 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=07774ae7-6d21-4646-8307-908dbae6fe03&question_id=d80199e9-eab8-444e-bfeb-b06dc91c6586&source_detail=9709%2F32+May%2FJune+2023) | | [**9709/33** May/June 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2023-may-june-9709-33/#q-11) | **Q11** Complex Number Argument and Exponential Form - CIE Pure Mathematics 3 2023 Jun Q11 | FRQ | 1 of 2 parts ((a)) | 6 of 9 on the paper | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=38715021-d2e9-4b06-9487-8984689a84e7&question_id=94305cbb-6703-4dd8-9bf3-242915736e28&source_detail=9709%2F33+May%2FJune+2023) | | [**9709/32** March 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2023-march-9709-32/#q-2) | **Q2** Argand Diagram Loci and Argument - CIE Pure Mathematics 2023 Mar Paper 32 Q2 | FRQ | 1 of 2 parts ((b)) | 2 of 5 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=fb85986e-2f5e-482c-8e08-173425b67cc3&question_id=b0bc512f-aba0-42e4-95f1-8efad9d410ae&source_detail=9709%2F32+March+2023) | | [**9709/32** October/November 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-october-november-9709-32/#q-5) | **Q5** Complex Roots Quadratic and Argand Diagram - CIE Pure Mathematics 2022 Nov Paper 32 Q5 | FRQ | 1 of 4 parts ((c)) | 3 of 8 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ec345ecb-a979-44f7-9e14-294a778ff934&question_id=3b6f5702-b418-4ff0-9bf0-f4b8a8ec961b&source_detail=9709%2F32+October%2FNovember+2022) | | [**9709/33** October/November 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-october-november-9709-33/#q-5) | **Q5** Argand Diagram Loci and Max Argument - CIE Pure Mathematics 3 | FRQ | 1 of 2 parts ((b)) | 2 of 6 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=955ef535-8636-46dc-9b2a-f083375bbec1&question_id=b5c2b05e-161b-4ac7-8222-2f08cd65d7d0&source_detail=9709%2F33+October%2FNovember+2022) | | [**9709/32** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-may-june-9709-32/#q-10) | **Q10** Complex Roots and Argand Locus - CIE Mathematics 2022 Jun Q10 | FRQ | 1 of 4 parts ((d)) | 2 of 11 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6ad396ce-ab9f-4c82-bba2-087b907a1ea1&question_id=520c30dd-cf32-438b-b3f8-c45c057ae272&source_detail=9709%2F32+May%2FJune+2022) | | [**9709/33** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-may-june-9709-33/#q-5) | **Q5** Argand Diagram Geometry and Inverse Tangent Identity - CIE A Level Mathematics 2022 Jun Paper 33 Q5 | FRQ | 1 of 3 parts ((c)) | 2 of 8 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9659571c-b4b6-458e-b3ff-de05ece281b2&question_id=1988e31b-3977-4b7e-9dfd-301927cb21f4&source_detail=9709%2F33+May%2FJune+2022) | | [**9709/32** March 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-march-9709-32/#q-6) | **Q6** Complex Numbers Equation with Conjugate - CIE A Level Mathematics 2022 Mar Paper 32 Q6 | FRQ | 1 part | 6 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=494ba528-51f5-41a2-babf-2cc4c40fecf4&question_id=bca7d440-fb21-4923-9ddb-1542c7c427ae&source_detail=9709%2F32+March+2022) | | [**9709/32** October/November 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2021-october-november-9709-32/#q-3) | **Q3** Complex Conjugates and Equations - CIE A-Level Mathematics 2021 Nov Paper 32 Q3 | FRQ | 2 parts ((a), (b)) | 6 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=e143fbb0-4c0c-42bd-8875-d51f745a2eeb&question_id=72a7a705-5d43-477b-ac72-bf23e7f66bd4&source_detail=9709%2F32+October%2FNovember+2021) | | [**9709/32** October/November 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2021-october-november-9709-32/#q-5) | **Q5** Argand Diagram Region and Maximum Argument - CIE A-Level Mathematics 2021 Nov Paper 32 Q5 | FRQ | 1 of 2 parts ((b)) | 3 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=e143fbb0-4c0c-42bd-8875-d51f745a2eeb&question_id=e63265b8-a6aa-4029-83d8-2eee1f7e3d3e&source_detail=9709%2F32+October%2FNovember+2021) | | [**9709/31** May/June 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2020-may-june-9709-31/#q-10) | **Q10** Complex Numbers and Argand Diagram Loci - CIE 2020 Jun Paper 31 Q10 | FRQ | 2 of 4 parts ((a)(ii), (b)(ii)) | 5 of 12 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=30d827e6-7a05-4ddb-93bb-64f6a01bb238&question_id=a705dab2-20ce-44b3-8d7b-857d50150068&source_detail=9709%2F31+May%2FJune+2020) | | [**9709/33** May/June 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2020-may-june-9709-33/#q-9) | **Q9** Complex Number Equations and Argand Diagram Loci - CIE Pure Mathematics 2020 Jun Q9 | FRQ | 1 of 2 parts ((a)) | 5 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ff5efdae-7baa-4c33-aa9c-f8b1c25c428d&question_id=6490af2a-8b44-4728-a551-413f5e6d1cd2&source_detail=9709%2F33+May%2FJune+2020) | | [**9709/32** March 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2020-march-9709-32/#q-10) | **Q10** Complex Simultaneous Equations and Locus - CIE Pure Mathematics 3 March 2020 Q10 | FRQ | 1 of 3 parts ((b)(ii)) | 2 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=11f225a5-63c6-446a-9114-463175a53c07&question_id=80107b80-6bc4-4d2d-88f7-58ff5f79930e&source_detail=9709%2F32+March+2020) | ## Related topic questions in Complex numbers - [• carry out operations of addition, subtraction, multiplication and division of two complex numbers expressed in Cartesian form $x+\mathrm{i}y$](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/carry-out-operations-of-addition-subtraction-multiplication-and-division-of-two/) — 32 question items · 30 papers — 136 marks · 2020–2026 - [• carry out operations of multiplication and division of two complex numbers expressed in polar form $r(\cos\theta+\mathrm{i}\sin\theta)\equiv r\mathrm{e}^{\mathrm{i}\theta}$](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/carry-out-operations-of-multiplication-and-division-of-two-complex-numbers-expressed/) — 14 question items · 11 papers — 35 marks · 2021–2026 - [• find the two square roots of a complex number](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/find-the-two-square-roots-of-a-complex-number/) — 10 question items · 10 papers — 51 marks · 2021–2026 - [• illustrate simple equations and inequalities involving complex numbers by means of loci in an Argand diagram](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/illustrate-simple-equations-and-inequalities-involving-complex-numbers-by-means-of/) — 50 question items · 31 papers — 156 marks · 2020–2026 - [• represent complex numbers geometrically by means of an Argand diagram](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/represent-complex-numbers-geometrically-by-means-of-an-argand-diagram/) — 26 question items · 21 papers — 80 marks · 2020–2026 - [• understand in simple terms the geometrical effects of conjugating a complex number and of adding, subtracting, multiplying and dividing two complex numbers](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/understand-in-simple-terms-the-geometrical-effects-of-conjugating-a-complex-number/) — 9 question items · 8 papers — 17 marks · 2021–2026 ## Topic question rules and edge cases **How many topic questions cover this syllabus point?** 27 question stems cover this subtopic across 25 papers, but only 32 tagged parts and 109 marks belong to it. Other parts of the same questions are assessed under different statements and are excluded from this page. **Which papers include this subtopic?** The table lists every matching session from 2020–2026. Each row links to the question anchor on the paper page, where the full paper context and practice entry point are available. **Why can one question appear under several subtopics?** The parts of one question can assess different syllabus statements. Each part is counted under its own subtopics, so the same question stem can appear on several subtopic pages while each page lists only the parts and marks tagged to that statement. **Can I practise these questions with AI marking?** Yes. Open a paper from the table and use the Interactive Practice Hub entry point. The page itself is static HTML so search engines and retrieval agents can read the full question list without executing JavaScript. --- Full page with native tables, bar charts and Practice Hub links: https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/understand-the-idea-of-a-complex-number-recall-the-meaning-of-the-terms-real-part/