# 9709 P3 Complex numbers Topic Questions

> CIE IAL 9709 P3: every Complex numbers topic question from 49 papers (2020–2026), grouped by syllabus point. 152 questions, 491 marks, with direct links…

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CIE IAL · Mathematics · 9709 P3 · A Level

Every 9709 P3 Complex numbers topic question from the 2020–2027 syllabus, drawn from 49 papers (2020–2026) and grouped by syllabus point. Each row opens a page listing the exact question numbers, marks and a direct link into the paper. These are questions by topic, not full papers, so you can revise one topic at a time.

- 9709 P3
- 8 subtopics
- 152 topic questions
- 49 papers
- 491 tagged marks
- [Back to Complex numbers](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/)
- [All paper codes](https://www.examsci.com/topics/)

Core finding

**illustrate simple equations and inequalities involving complex… is the most frequently assessed subtopic in Complex numbers, with 50 topic questions and 156 marks across 31 papers.** carry out operations of addition, subtraction… follows with 32 topic questions and 136 marks. The topic contains 8 subtopics, 152 topic questions and 491 marks in total. Rows count only the parts tagged to that subtopic, keep the same colour in both charts and repeat paper count, tagged marks and year range in the native table.

## Topic question count and mark distribution

Subtopics are on the vertical axis and sorted from highest to lowest. Only the parts whose knowledge graph matches a subtopic are counted for it, and percentages are each row's share of the tagged total in that chart. A part tagged to several subtopics is counted in each bar, so the bars are not a partition of the topic total.

### Questions by subtopic

question items

- [• 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/) (31 papers) — 50 · 27.9%
- [• 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/) (30 papers) — 32 · 17.9%
- [• 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](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/) (25 papers) — 32 · 17.9%
- [• 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/) (21 papers) — 26 · 14.5%
- [• 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/) (11 papers) — 14 · 7.8%
- [• 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 papers) — 10 · 5.6%
- [• 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/) (8 papers) — 9 · 5.0%
- [• use the result that, for a polynomial equation with real coefficients, any non-real roots occur in conjugate pairs](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/use-the-result-that-for-a-polynomial-equation-with-real-coefficients-any-non-real/) (5 papers) — 6 · 3.4%

### Marks by subtopic

marks

- [• 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/) (31 papers) — 156 · 25.6%
- [• 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/) (30 papers) — 136 · 22.3%
- [• 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](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/) (25 papers) — 109 · 17.9%
- [• 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/) (21 papers) — 80 · 13.1%
- [• 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 papers) — 51 · 8.4%
- [• 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/) (11 papers) — 35 · 5.7%
- [• use the result that, for a polynomial equation with real coefficients, any non-real roots occur in conjugate pairs](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/use-the-result-that-for-a-polynomial-equation-with-real-coefficients-any-non-real/) (5 papers) — 25 · 4.1%
- [• 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/) (8 papers) — 17 · 2.8%

## Subtopic comparison matrix

Curriculum order is by syllabus number, then alphabetically. Every row links to the matching past-paper question list.

| Subtopic | Topic questions | Papers | Marks | Years | |
| --- | --- | --- | --- | --- | --- |
| **[• 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 | 30 | 136 | 2020–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/carry-out-operations-of-addition-subtraction-multiplication-and-division-of-two/) |
| **[• 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 | 11 | 35 | 2021–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/carry-out-operations-of-multiplication-and-division-of-two-complex-numbers-expressed/) |
| **[• 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 | 10 | 51 | 2021–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/find-the-two-square-roots-of-a-complex-number/) |
| **[• 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 | 31 | 156 | 2020–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/illustrate-simple-equations-and-inequalities-involving-complex-numbers-by-means-of/) |
| **[• 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 | 21 | 80 | 2020–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/represent-complex-numbers-geometrically-by-means-of-an-argand-diagram/) |
| **[• 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 | 8 | 17 | 2021–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/understand-in-simple-terms-the-geometrical-effects-of-conjugating-a-complex-number/) |
| **[• 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](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/)** | 32 | 25 | 109 | 2020–2026 | [Open topic questions](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/) |
| **[• use the result that, for a polynomial equation with real coefficients, any non-real roots occur in conjugate pairs](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/use-the-result-that-for-a-polynomial-equation-with-real-coefficients-any-non-real/)** | 6 | 5 | 25 | 2020–2025 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/use-the-result-that-for-a-polynomial-equation-with-real-coefficients-any-non-real/) |

## Browse every topic question

- [• 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
- [• 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](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/) — 32 question items · 25 papers — 109 marks · 2020–2026
- [• use the result that, for a polynomial equation with real coefficients, any non-real roots occur in conjugate pairs](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/complex-numbers/use-the-result-that-for-a-polynomial-equation-with-real-coefficients-any-non-real/) — 6 question items · 5 papers — 25 marks · 2020–2025

## Other topics in 9709 P3

- [Algebra 156 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/algebra/)
- [Differential equations 75 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differential-equations/)
- [Differentiation 134 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/differentiation/)
- [Integration 114 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/integration/)
- [Logarithmic and exponential functions 68 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/logarithmic-and-exponential-functions/)
- [Numerical solution of equations 131 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/numerical-solution-of-equations/)
- [Trigonometry 138 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/)
- [Vectors 133 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/vectors/)

## Topic question rules and edge cases

**How many subtopics does Complex numbers contain?**

This page lists 8 subtopics tagged to the current syllabus. They are ordered by syllabus number, then alphabetically, and each row opens a page of matching past-paper questions.

**How are the subtopic question and mark totals calculated?**

A multiple-choice question contributes one item and its marks to every subtopic it is tagged with. A structured question contributes one item per tagged part, and that part’s marks; untagged parts of the same question are not counted here. A part tagged to several subtopics therefore appears under each of them.

**Why do some subtopics have no numbered prefix?**

Practical-skills statements and some syllabus bullets are unnumbered. Numbered statements come first; unnumbered statements and ties are sorted alphabetically.

**Is the LaTeX rendered without JavaScript?**

Yes. Subtopics that contain formulas are converted to static KaTeX HTML during the build, and the KaTeX stylesheet is served from the same site.

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