Complex Numbers

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ASFM – Core – Intro to Complex Numbers

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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1A/B Slides (Courtesy of Owen134866)

Complex Numbers 1 • What are imaginary numbers? Simple calculations • CP1 Ex1A • 🏅

Complex Numbers 2 • Solving Quadratic Equations • CP1 Ex1B • 🏅

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 1-8

Extra Questions

• Dr Frost Questions (Includes 1C as well)

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 664a: Simplify the square root of a negative number. (not yet active)
• 664b: Calculate i^k for any positive integer k (not yet active)
• 664c: Calculate (ai)^k for any positive integer k and real a (not yet active)
• 665a: Add or subtract two complex numbers. (not yet active)
• 665b: Simplify a complex expression involving a single bracket expansion. (not yet active)
• 667a: Divide a complex number by an integer. (not yet active)
• 664: Exam Practice: Understanding imaginary numbers
• 665: Exam Practice: Adding, subtracting and multiplying complex numbers
• 667: Exam Practice: Division of complex numbers

Videos & Other Multimedia

How Imaginary Numbers Were Invented

How Imaginary Numbers were Invented by Veritasium

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Tarsia dominoes pdf and solutions
• Andy Lutwyche
  • Introduction to Imaginary
• Math = Love (Sarah Carter)
  • Powers of i Odd One Out
  • Powers of i factorials task
  • Powers of i activity
  • Complex Numbers Foldable
• Open Middle
  • Complex Number Tasks
• The Chalkface
  • Inventing Imaginary Numbers: PDF
• Ben Sparks (GeoGebra)
  • Complex Addition Arithmagon: GeoGebra

ASFM – Core – Multiplying Complex Numbers

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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1C Slides (Courtesy of Owen134866)

Complex Numbers 3 • Multiplying with Complex Numbers • CP1 Ex1C • 🏅

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 9-11

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

• 665c: Multiply two complex numbers. (not yet active)
• 665d: Square a complex number. (not yet active)
• 665e: Multiply three complex numbers. (not yet active)
• 665f: Expand and simplify (a+bi)ⁿ for positive integer n (not yet active)
• 665g: Expand and simplify (a-bi)ⁿ for positive integer n (not yet active)
• 665: Exam Practice: Adding, subtracting and multiplying complex numbers

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• WW quick questions Word Doc or PDF
• MadAsMaths (T. Madas)
  • Complex Numbers Part 1 Exam Questions Q5, 12, 20, 27, 46 (difficulty 2–3 of 5)
  • Complex Numbers Part 1 Basic Complex Algebra Q7–10, 26

ASFM – Core – Complex Conjugates

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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1D Slides (Courtesy of Owen134866)

Complex Numbers 4 • Complex Conjugation • CP1 Ex1D • 🏅

Complex Numbers 5 • ‘Realising’ the Denominator • CP1 Ex1D • 🏅

Complex Numbers 6 • Square Roots of Complex Numbers • CP1 ExtraQs • 🏅

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 12-16

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

• 666a: Write the conjugate of a complex number z^* (or barz). (not yet active)
• 666b: Determine z + z^* (not yet active)
• 666c: Determine zz^* (not yet active)
• 666d: Solve an equation involving both z and z^* (not yet active)
• 667b: Divide a complex number by another complex number.
• 666: Exam Practice: Complex conjugation
• 667: Exam Practice: Division of complex numbers

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

ASFM – Core – Complex Roots of Quadratic Equations

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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1E Slides (Courtesy of Owen134866)

Complex Numbers 7 • Roots of Quadratics • CP1 Ex1E • 🏅

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (Up to 18:45)

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 17-21

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

• 668a: Given a complex root of a quadratic equation, state the other root. (not yet active)
• 668b: Solve quadratic equations with complex roots.
• 668c: Determine a quadratic equation given one of its complex roots.
• 668d: Factorise the sum of squares using complex numbers. (not yet active)
• 668e: Know the Fundamental Theorem of Algebra. (not yet active)
• 668: Exam Practice: Solving quadratic equations to find potentially complex roots

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheet & Activities

• MEI activities from old FP1

ASFM – Core – Complex Roots of Cubics and Quartics

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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1F Slides (Courtesy of Owen134866)

Complex Numbers 8 • Roots of Cubics & Quartics • CP1 Ex1F • 🏅

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (From 18:45)

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 22-27

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

• 669a: State the number of real roots and complex roots of a cubic graph given its sketch. (not yet active)
• 669b: State the number of real roots and complex roots of a quartic graph given its sketch. (not yet active)
• 669c: Given a complex root of a cubic or quartic equation, state another root. (not yet active)
• 669d: Determine the 3 roots of a cubic equation given factorisation into a linear and quadratic factor. (not yet active)
• 669e: Determine the 4 roots of a quartic equation given factorisation into two quadratic factors. (not yet active)
• 669f: Verify a complex root of a cubic or quartic equation. (not yet active)
• 669g: Solve a cubic equation with complex roots, given its real root.
• 669h: Determine a cubic equation given a real root and a complex root. (not yet active)
• 669i: Determine a quartic equation given a real root and a complex root. (not yet active)
• 669j: Determine a quartic equation given two of its (non-conjugate) roots. (not yet active)
• 669k: Determine the constant term in a quartic equation given a real root. (not yet active)
• 669l: Solve a quartic equation given one of its complex roots. (not yet active)
• 669m: Determine the 3 other roots of a quartic equation given one complex root and some coefficients of the quartic unknown. (not yet active)
• 669: Exam Practice: Solving cubic and quartic equations to find potentially complex roots

Enrichment Video

Fundamental Theorem of Algebra – Numberphile

Numberphile: Fundamental Theorem of Algebra

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

External whole topic past paper style questions

• WW Dr Frost Style QQQs (Version 1) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
• WW Dr Frost Style QQQs (Version 2) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
• Advanced Highers Matrices Exam Questions & Answers
• Pret Homework (@MathedUp)
  • Complex Numbers (@MathedUp, ppt)
• Susan Wall (Active A-level Maths)
  • Complex Numbers: Sometimes, Always, Never (Susan Wall;

Activities

• Math = Love (Sarah Carter)
  • Imaginary & Complex Numbers activities
• NRICH (student problems)
  • Complex Numbers (Further)
• The Chalkface
  • iSum: PDF
• Andy Lutwyche
  • Simplifying Codebreaker
  • Roots of Polynomials Codebreaker
  • Roots of Quadratics Codebreaker

Worksheets

• MathedUp
  • Complex numbers 1: Questions · Challenge · Answers
• Jethwa Maths
  • 10 Minute Starters: Complex Numbers 2
• Physics & Maths Tutor
  • CP1 Ch.1 Complex Numbers: Questions by topic
• MadAsMaths (T. Madas)
  • Complex Numbers Part 1 Exam Questions Q43, 62, 63, 66, 67 (difficulty 3–4 of 5)
• Dr Austin Maths
  • Calculating Fill in the Blanks (Word | PDF | Answers)
  • Solving Quadratics, Cubics and Quartics Crack the Code (Word | PDF | Answers)