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Contents
- Whole Topic Notes
- 2A Introduction to Argand Diagrams
- 2B Modulus & Argument
- 2C Modulus-Argument Form
- 2D Multiplying & Dividing in Modulus-Argument Form
- 2E Loci on Argand Diagrams
- 2F Shading Regions on Argand Diagrams
- Whole Topic Summary Resources (Including Past Paper Questions)
Whole Topic Notes
Download Full Topic Slides
- Textbook Notes as PPTs (Courtesy of Owen134866)
Full Notes to Accompany Slides
Dr Frost
- Dr Frost AS Core Pure Argand Diagrams Section
- Dr Frost AS Core Pure Argand Diagrams Slides
- Blank Notes to Follow Slides Word Doc or PDF (Courtesy of King’s Chester Maths Department)
Acute Learning Whole Chapter Problem Pairs
Notes
- Physics & Maths Tutor
- CP1 Ch.2 Argand Diagrams: Cheat sheet
2A Introduction to Argand Diagrams
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
No Live Lesson from Bicen Maths Yet
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 670a: Plot a complex number on an argand diagram. (not yet active)
- 670b: Read off a complex number plotted on an argand diagram. (not yet active)
- 670c: Plot the conjugate z^* of a complex number z on an argand diagram. (not yet active)
- 670e: Determine the midpoint of two complex numbers on an Argand diagram. (not yet active)
- 670f: Determine the distance between two points on an Argand diagram. (not yet active)
- 670: Exam Practice: Argand diagrams
Other resources
Courtesy of Numberphile
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Online Platform
- Ben Sparkes Geogebra Resources (Do watch the numberphile video on the left to get a good idea of how to work through these).
Online Platforms
- Khan Academy
- The complex plane (Argand diagram): Videos & practice
2B Modulus & Argument
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Tutorial Videos
Complex Numbers : Modulus and Argument | ExamSolutions by ExamSolutions
A-Level Further Maths B5-01 Complex Numbers: Introducing the Modulus and Argument by TLMaths
A-Level Further Maths B5-02 Complex Numbers: Examples of finding the Modulus and Argument by TLMaths
Finding the Modulus and Argument of a Complex Number by Jack's Maths
Dr Frost resources
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 670d: Determine the modulus ≤ft|zright| of a complex number. (not yet active)
- 670g: Determine the argument textarg(z) of a complex number in the first quadrant. (not yet active)
- 670h: Determine the argument textarg(z) of a complex number in the second quadrant. (not yet active)
- 670i: Determine the argument textarg(z) of a complex number in the third or fourth quadrants. (not yet active)
- 670j: Determine the argument of a complex number that requires prior calculation. (not yet active)
- 670k: Determine an unknown constant in a complex expression with a given modulus. (not yet active)
- 670l: Determine an unknown constant in a complex expression with a given argument. (not yet active)
- 670: Exam Practice: Argand diagrams
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Online Platform
- Bossmaths interactive 2×2 transformations and questions
Online Platforms
- Khan Academy
- Modulus & argument: Videos & practice
Worksheets
- MadAsMaths (T. Madas)
- Complex Numbers Part 1 Exam Questions Q1, 8, 9, 45, 50, 81, 83 (difficulty 2–5 of 5)
- Complex Numbers Part 1 Modulus and Argument Q1–3, 7
2C Modulus-Argument Form
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Tutorial Videos
Complex Numbers : Mod-Arg form r[cos(x)+isin(x)] : ExamSolutions by ExamSolutions
A-Level Further Maths B5-03 Complex Numbers: Introducing Modulus-Argument Form by TLMaths
A-Level Further Maths B5-04 Complex Numbers: Cartesian to Modulus-Argument Form by TLMaths
A-Level Further Maths B5-05 Complex Numbers: Modulus-Argument Form to Cartesian by TLMaths
Dr Frost resources
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 671a: Convert a complex number from Cartesian to modulus-argument form. (not yet active)
- 671b: Convert a complex number from modulus-argument form into Cartesian/rectangular form. (not yet active)
- 671c: Write r(cos θ – i sin θ) in modulus argument form and recognise as the conjugate. (not yet active)
- 671: Exam Practice: Conversion between Cartesian (rectangular) and modulus-argument (polar) form
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Online Platform
- Bossmaths interactive 3×3 transformations and questions
Activities
- The Chalkface
- Complex Number Forms: Excel (if macros are blocked: right-click the file › Properties › tick Unblock)
Online Platforms
- Khan Academy
- Modulus-argument (polar) form: Videos & practice
2D Multiplying & Dividing in Modulus-Argument Form
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Tutorial Videos
Multiplication Rule for the Mod-Arg of two Complex Numbers : ExamSolutions Maths Tutorials by ExamSolutions
Multiplication & Division of Complex Numbers in Mod-Arg form Examples : ExamSolutions by ExamSolutions
A-Level Further Maths B6-02 Complex Numbers: Multiplying Complex Numbers in Modulus-Argument Form by TLMaths
Dr Frost resources
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 672a: Determine the modulus of the product of two complex numbers in modulus-argument form. (not yet active)
- 672b: Determine the modulus of the product of two complex numbers in a mixture of Cartesian and modulus-argument form. (not yet active)
- 672c: Determine the modulus of the division of two complex numbers in a mixture of Cartesian and modulus-argument form. (not yet active)
- 672d: Determine the argument of the product of two complex numbers in modulus-argument form, where one is in the form cos θ – i sin θ (not yet active)
- 672e: Determine the product of two complex numbers in modulus-argument form where one is given in Cartesian/rectangular form and the other in modulus-argument form. (not yet active)
- 672f: Determine the division of two complex numbers in modulus-argument form where one is given in Cartesian/rectangular form and the other in modulus-argument form. (not yet active)
- 672g: Understand the geometrical effects of multiplying and dividing two complex numbers on an Argand diagram. (not yet active)
- 672h: Determine a complex number z1 where z2 is given along with the argument and modulus of their product. (not yet active)
- 672: Exam Practice: Multiplying and dividing complex numbers in modulus-argument form
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Online Platform
- Bossmaths interactive 2×2 transformations and questions
Worksheet & Activities
- MEI activities from old FP1
Online Platforms
- Khan Academy
- Multiplying, dividing & powers in polar form: Videos & practice
Worksheets
- MadAsMaths (T. Madas)
- Complex Numbers Part 1 Exam Questions Q21, 25, 31, 56, 61 (difficulty 2–4 of 5)
- Complex Numbers Part 1 Modulus and Argument Q4–6, 8, 9
2E Loci on Argand Diagrams
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 673a: Sketch the locus of points z such that ≤ft|zright| = r (not yet active)
- 673b: Sketch the locus of points z such that ≤ft|zright| – z1| = r (not yet active)
- 673c: Sketch the locus of points on an argand diagram where ≤ft|z – z1right| = ≤ft|z – z2right| (not yet active)
- 673d: Determine the Cartesian equation of a locus of points z constrained by ≤ft|z – z1right| = ≤ft|z – z2right| (not yet active)
- 673e: Sketch a locus of points z where textrmarg(z) = k (not yet active)
- 673f: Sketch a locus of points z where textrmarg(z – z1) = k (not yet active)
- 673g: Determine the Cartesian equation of the locus of points z where arg(z – z1) = k (not yet active)
- 673i: Determine the maximum or minimum value for textrmarg(z) given that ≤ft|z – z1right| = r (not yet active)
- 673j: Determine the maximum or minimum value for ≤ft|zright| given that ≤ft|z – z1right| = r (not yet active)
- 673: Exam Practice: Simple loci in an Argand diagram
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- Tom Button Geogebra locus for |z-w|=3
- Desmos
- Complex Loci (by Jo Hill)
Worksheets
- Mathshelper (Jon Stone)
- MadAsMaths (T. Madas)
- Complex Numbers Part 2 Exam Questions Q5, 18, 28, 34, 36, 40, 43, 45, 50, 55, 67, 69, 72, 73, 83, 96, 120, 121, 177 (difficulty 2–5 of 5)
- Complex Numbers Part 2 Complex Loci Q2, 8, 11, 12, 14–16
2F Shading Regions on Argand Diagrams
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Tutorial Videos
Complex Numbers – Loci : Regions : ExamSolutions Maths Video Tutorials by ExamSolutions
A-Level Further Maths B7-03 Argand Diagram: Inequalities with Circles by TLMaths
A-Level Further Maths B7-06 Argand Diagram: Inequalities with Perpendicular Bisectors by TLMaths
Dr Frost resources
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Worksheets
- MadAsMaths (T. Madas)
- Complex Numbers Part 2 Exam Questions Q1, 9, 11, 23, 25, 32, 152, 166 (difficulty 2–4 of 5)
- Complex Numbers Part 2 Complex Loci Q1, 5, 6, 10, 17
Whole Topic Summary Resources (Including Past Paper Questions)
Download PPQs as WW Powerpoint for Core Pure Complex Numbers
External Whole Topic Past Paper Style Questions
- WW Dr Frost Style QQQs Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
- WW Dr Frost Style QQQs Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.) v2
Activities
- NRICH (student problems)
- Korovatron
Worksheets
- Jethwa Maths
- 10 Minute Starters: Argand Diagrams
- Physics & Maths Tutor
- CP1 Ch.2 Argand Diagrams: Questions by topic
- MadAsMaths (T. Madas)
- Complex Numbers Part 1 Exam Questions Q59, 74, 77 (difficulty 4–5 of 5)
- Dr Austin Maths
✦ Links marked ✦ are also featured and recommended by Jo Morgan on Resourceaholic.