More Complex Numbers

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A2FM – Core – Exponential Form of Complex Numbers

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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1A Slides (Courtesy of Owen134866)

Complex Numbers (Year 2) 1 • Recap of Year 1 • CP2 Ex1A • 🎯

Complex Numbers (Year 2) 2 • Exponential Form • CP2 Ex1A • 🎯

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 1-9

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

• 718a: Convert a complex number from modulus-argument form to exponential form. (not yet active)
• 718b: Convert a complex number from Cartesian/rectangular form to exponential form. (not yet active)
• 718c: Convert an exponential term e^iθ to modulus-argument form. (not yet active)
• 718d: Convert an exponential term e^-iθ to cosθ – isinθ form. (not yet active)
• 718: Exam Practice: Euler’s formula e^iθ = cos(θ) + i sin(θ) (not yet active)

Other Videos & Multimedia

Euler's Formula – Numberphile

Numberphile ‘Euler’s Formula’

Enrichment Video

e^(iπ) in 3.14 minutes, using dynamics | DE5

3Blue1Brown: e^(iπ) in 3.14 minutes, using dynamics

e to the pi i for dummies

Mathologer: e to the pi i for dummies

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platform

• Bossmaths interactive 2×2 transformations and questions

A2FM – Core – Multiplying and Dividing Complex Numbers

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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1B Slides (Courtesy of Owen134866)

Complex Numbers (Year 2) 3 • Multiplying and Dividing • CP2 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 10-13

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

• 719c: Simplify an expression involving multiplication, division and powers of complex numbers in modulus-argument form, including cosθ – isinθ form. (not yet active)
• 719: Exam Practice: Powers of complex numbers using de Moivre’s theorem

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platform

• Bossmaths interactive 2×2 transformations and questions

A2FM – Core – De Moivre's Theorem

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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1C Slides (Courtesy of Owen134866)

Complex Numbers (Year 2) 4 • De Moivre’s Theorem • CP2 Ex1C • 🎯

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 14-18

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

• 719a: Prove de Moivre’s theorem by induction. (not yet active)
• 719b: Use de Moivre’s theorem to find a power of complex numbers in modulus-argument form. (not yet active)
• 719d: Use de Moivre’s theorem to find a power of complex numbers in Cartesian/rectangular form. (not yet active)
• 719: Exam Practice: Powers of complex numbers using de Moivre’s theorem

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platform

• Bossmaths interactive 3×3 transformations and questions

A2FM – Core – Using de Moivre's Theorem to Prove Trigonometric Identities

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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1D Slides (Courtesy of Owen134866)

Textbook Questions

1 a, b, c, 2, 6 & 7 if only looking at first type

Complex Numbers (Year 2) 5 • Express sin/cos(nx) as powers of sin/cos • CP2 Ex1D • 🎯

Complex Numbers (Year 2) 6 • Expressing powers of sin/cos in terms of sin/cos(nx) • CP2 Ex1D • 🎯

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 19-26

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

• 720a: Write sin kx or cos kx as sum of powers of sin or cos (not yet active)
• 720b: Write a power of sin x or cos x as a sum of sin(kx) or cos(kx) terms. (not yet active)
• 720c: Integrate powers of trigonometric terms where cubed or of a higher power. (not yet active)
• 720d: Solve an equation given in the form sin ax = b sin cx (not yet active)
• 720: Exam Practice: Proving trigonometric identities using de Moivre’s theorem

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

A2FM – Core – Sum of Complex Number Series – Part 1 Finite Summations

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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1E Part 1 Slides (Courtesy of Owen134866)

Complex Numbers (Year 2) 7 • Sums of Series pt.1 • CP2 Ex1E • 🎯

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 27-33

Extra Questions

• Dr Frost Questions (Very short quiz: 3 questions)

Key Skills

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

• 721a: Write an expression in the form fracke^iθ – 1 in terms of trigonometric terms. (not yet active)
• 721b: Simplify the sum of a finite geometric series of complex terms. (not yet active)
• 721c: Simplify a finite series of sin(kθ) terms or cos(kθ) terms by use of de Moivre’s theorem. (not yet active)
• 721: Exam Practice: Sums of series using de Moivre’s theorem

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

A2FM – Core – Sum of Complex Number Series – Part 2 Infinite Summations

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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1E Part 2 Slides Not Yet Available

Complex Numbers (Year 2) 8 • Sums of Series pt.2 • CP2 Ex1E • 🎯

Complex Numbers (Year 2) 9 • Sums of Series pt.3 • CP2 Ex1E • 🎯

Complex Numbers (Year 2) 10 • Sums of Series pt.4 • CP2 Ex1E • 🎯

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• No Dr Frost 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

• 721d: Simplify a infinite series of sin(kθ) terms or cos(kθ) terms by use of de Moivre’s theorem. (not yet active)
• 721: Exam Practice: Sums of series using de Moivre’s theorem

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

External Whole Topic Past Paper Style Questions

• WW Dr Frost Style QQQs Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)

Activities

• NRICH (student problems)
  • Complex Numbers (Further)

Worksheets

• MathedUp
  • Complex numbers 2: Questions · Challenge · Answers
• Physics & Maths Tutor
  • CP2 Ch.1 Complex Numbers: Questions by topic
• Dr Austin Maths
  • Different Forms Fill in the Blanks (Word | PDF | Answers)
  • Multiplying and Dividing Exponential Form Match-Up (Word | PDF | Answers)
  • Investigating Powers Activity (Word | PDF | Answers)
  • De Moivre's Theorem Fill in the Blanks (Word | PDF | Answers)