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 31 papers

5027.9%

• carry out operations of addition, subtraction, multiplication and division of two complex numbers expressed in Cartesian form

x + i y

30 papers

3217.9%

• 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 25 papers

3217.9%

• represent complex numbers geometrically by means of an Argand diagram 21 papers

2614.5%

• carry out operations of multiplication and division of two complex numbers expressed in polar form

r (cos θ + i sin θ) \equiv r e^{i θ}

11 papers

147.8%

• find the two square roots of a complex number 10 papers

105.6%

• understand in simple terms the geometrical effects of conjugating a complex number and of adding, subtracting, multiplying and dividing two complex numbers 8 papers

95.0%

• use the result that, for a polynomial equation with real coefficients, any non-real roots occur in conjugate pairs 5 papers

63.4%

Marks by subtopic

marks

• illustrate simple equations and inequalities involving complex numbers by means of loci in an Argand diagram 31 papers

15625.6%

• carry out operations of addition, subtraction, multiplication and division of two complex numbers expressed in Cartesian form

x + i y

30 papers

13622.3%

• 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 25 papers

10917.9%

• represent complex numbers geometrically by means of an Argand diagram 21 papers

8013.1%

• find the two square roots of a complex number 10 papers

518.4%

• carry out operations of multiplication and division of two complex numbers expressed in polar form

r (cos θ + i sin θ) \equiv r e^{i θ}

11 papers

355.7%

• use the result that, for a polynomial equation with real coefficients, any non-real roots occur in conjugate pairs 5 papers

254.1%

• understand in simple terms the geometrical effects of conjugating a complex number and of adding, subtracting, multiplying and dividing two complex numbers 8 papers

172.8%

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 $x + i y$	32	30	136	2020–2026	Open topic questions
• carry out operations of multiplication and division of two complex numbers expressed in polar form $r (cos θ + i sin θ) \equiv r e^{i θ}$	14	11	35	2021–2026	Open topic questions
• find the two square roots of a complex number	10	10	51	2021–2026	Open topic questions
• illustrate simple equations and inequalities involving complex numbers by means of loci in an Argand diagram	50	31	156	2020–2026	Open topic questions
• represent complex numbers geometrically by means of an Argand diagram	26	21	80	2020–2026	Open topic questions
• understand in simple terms the geometrical effects of conjugating a complex number and of adding, subtracting, multiplying and dividing two complex numbers	9	8	17	2021–2026	Open 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	32	25	109	2020–2026	Open topic questions
• use the result that, for a polynomial equation with real coefficients, any non-real roots occur in conjugate pairs	6	5	25	2020–2025	Open topic questions

Browse every topic question

• carry out operations of addition, subtraction, multiplication and division of two complex numbers expressed in Cartesian form $x + i y$ 32 question items · 30 papers 136 marks · 2020–2026 • carry out operations of multiplication and division of two complex numbers expressed in polar form $r (cos θ + i sin θ) \equiv r e^{i θ}$ 14 question items · 11 papers 35 marks · 2021–2026 • 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 50 question items · 31 papers 156 marks · 2020–2026 • 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 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 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 6 question items · 5 papers 25 marks · 2020–2025

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.

9709 P3 Complex numbers Topic Questions