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3rd April

3rd April: Complex Numbers

Learning Outcomes

Number systems:
Students working at OL should be able to:

  • investigate the operations of addition, multiplication, subtraction and division with complex numbers C in rectangular form a+ib
  • illustrate complex numbers on an Argand diagram
  • interpret the modulus as distance from the origin on an Argand diagram and calculate the complex conjugate

Students working at HL should be able to:

  • calculate conjugates of sums and products of complex numbers

Algebra:
Students working at HL should be able to:

  • use the Conjugate Root Theorem to find the roots of polynomials
  • work with complex numbers in rectangular and polar form to solve quadratic and other equations including those in the form zn = a, where n ∈ Z and z = r (Cos θ + iSin θ )
  • use De Moivre’s Theorem
Teaching & Learning Plans
Workshop Materials
Operations - Geogebra Files
Polar Form & DeMoivre’s Theorem
SEC Exam Questions

Complex Number Operations - Plan

https://www.scoilnet.ieuploads/resources/29639/29375.pdf Added: 16 May 2019 Contributor: PDST Resource type: Lesson Plan

To familiarise students with operations on Complex Numbers and to give an algebraic
and geometric interpretation to these operations

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Strand: 3. Number

Strand unit: 1. Number Systems (Complex Numbers,Sequences)

Suggestions for use: To introduce students to the operations of complex numbers. To show that multiplication of a Complex Number by another Complex Number corresponds to a rotation and a scaling of the Complex Number.

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Complex Number Operations - Plan

https://www.scoilnet.ieuploads/resources/29638/29374.ppt Added: 16 May 2019 Contributor: PDST Resource type: Lesson Plan / Presentation

To familiarise students with operations on Complex Numbers and to give an algebraic
and geometric interpretation to these operations

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Strand: 3. Number

Strand unit: 1. Number Systems (Complex Numbers,Sequences)

Suggestions for use: To give students a deeper understanding of the operations of complex numbers. show that multiplication of a Complex Number by another Complex Number corresponds to a rotation and a
scaling of the Complex Number

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Complex Numbers Workshop

https://www.scoilnet.ieuploads/resources/32449/32191.pptx Added: 02 Apr 2020 Contributor: PDST Resource type: Demonstration / Guide/notes / Presentation

This presentation is the Complex Numbers sections of a Numbers workshop presented by the PDST. It focusses on the geometric view of complex numbers.

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Strand: 3. Number

Strand unit: 1. Number Systems (Complex Numbers,Sequences)

Suggestions for use: This can be used to introduce a geometric view of complex numbers, building on a students' prior knowledge of number to give them an understanding of complex numbers.

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Complex Numbers Workshop booklet

https://www.scoilnet.ieuploads/resources/32450/32192.docx Added: 02 Apr 2020 Contributor: PDST Resource type: Worksheet / Help Sheets / Activity

This booklet is best used with the Complex Numbers Workshop presentation and contains activities to work through to help gain an understanding of the geometric view of complex numbers.

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Strand: 3. Number

Strand unit: 1. Number Systems (Complex Numbers,Sequences)

Suggestions for use: Use with the Complex Numbers Workshop presentation to complete activities and gain a better understanding of the geometric view of complex numbers.

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The Argand Diagram and the Modulus of a Complex Number

https://www.scoilnet.ie/pdst/maths/...lc/lc-numbers/complexnumbersargand/ Added: 09 Nov 2019 Contributor: PDST Resource type: Guide/notes / Simulation

A GeoGebra file and student worksheet to investigate the Argand diagram and modulus of complex numbers.

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Strand: 4. Algebra

Strand unit: 4. Complex Numbers(Conjugate Root+De Moivre)

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Multiplying a complex number by a constant

https://www.geogebra.org/classic/hqc5kfft Added: 02 Apr 2020 Contributor: PDST Resource type: Demonstration / Simulation / Tool

This GeoGebra file invites students to explore what happens when a complex number is multiplied by a constant.

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Strand: 4. Algebra

Strand unit: 4. Complex Numbers(Conjugate Root+De Moivre)

Suggestions for use: GeoGebra file to explore the multiplication of a complex number by a constant

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Multiplying a complex number by i

https://www.geogebra.org/classic/q8mj3eym Added: 02 Apr 2020 Contributor: PDST Resource type: Demonstration / Simulation / Tool

This GeoGebra file allows the exploration of multiplying a complex number by i and by exponents of i.

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Strand: 4. Algebra

Strand unit: 4. Complex Numbers(Conjugate Root+De Moivre)

Suggestions for use: This GeoGebra file should be used to explore what happens to a complex number when it is multiplied by i or an exponent of i.

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Addition of complex numbers

https://tinyurl.com/WS4task2demo Added: 02 Apr 2020 Contributor: PDST Resource type: Demonstration / Simulation / Tool

GeoGebra file to allow the exploration of addition of complex numbers

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Strand: 4. Algebra

Strand unit: 4. Complex Numbers(Conjugate Root+De Moivre)

Suggestions for use: This GeoGebra file can be used to explore what happens when two complex numbers are added together, students will see a geometric view of the addition of complex numbers.

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Complex conjugate

https://www.geogebra.org/classic/wrxxyrsf Added: 02 Apr 2020 Contributor: PDST Resource type: Demonstration / Simulation / Tool

GeoGebra file to explore the conjugate of a complex number

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Strand: 4. Algebra

Strand unit: 4. Complex Numbers(Conjugate Root+De Moivre)

Suggestions for use: Use as a demonstration or an exploration tool for the geometric view of the complex conjugate.

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Multiplication of complex numbers

https://www.geogebra.org/classic/bmedez74 Added: 02 Apr 2020 Contributor: PDST Resource type: Demonstration / Simulation / Tool

The GeoGebra file can be used to explore the geometric view of a complex number multiplied by another complex number

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Strand: 4. Algebra

Strand unit: 4. Complex Numbers(Conjugate Root+De Moivre)

Suggestions for use: This file can be used to explore the multiplication of complex numbers.
It could also be used when introducing students to DeMoivre's theorem.

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Polar form & DeMoivre's theorem

https://www.scoilnet.ieuploads/resources/32467/32209.pptx Added: 02 Apr 2020 Contributor: PDST Resource type: Presentation

This presentation is created to guide students through the polar form of a complex number to introduce DeMoivre's theorem

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Strand: 4. Algebra

Strand unit: 4. Complex Numbers(Conjugate Root+De Moivre)

Suggestions for use: Use with the GeoGebra file (attached in presentation) 'multiplication of a complex number' to use the argument and modulus to guide students to get the polar form of a complex number and then to introduce DeMoivre's theorem.

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Student activity - Argument & Modulus

https://www.scoilnet.ieuploads/resources/32469/32211.pdf Added: 02 Apr 2020 Contributor: PDST Resource type: Worksheet / Activity

This worksheet should be used with the GeoGebra file (link in document) to encourage students to explore the relationship between the argument and the modulus when multiplying complex numbers.

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Strand: 4. Algebra

Strand unit: 4. Complex Numbers(Conjugate Root+De Moivre)

Suggestions for use: Worksheet to explore the relationship between the argument and the modulus when multiplying complex numbers. This could also be used to introduce DeMoivre's theorem.

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Language: English
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SEC 2019 HL p1 Q5 Complex Numbers

https://www.scoilnet.ieuploads/resources/32471/32213.pdf Added: 02 Apr 2020 Contributor: PDST Resource type: Exam Papers

SEC exam question on complex numbers

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Mathematics

Strand: 4. Algebra

Strand unit: 4. Complex Numbers(Conjugate Root+De Moivre)

Suggestions for use: Past exam question to assess understanding of complex numbers.

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SEC 2019 OL p1 Q2 Complex Numbers

https://www.scoilnet.ieuploads/resources/32472/32214.pdf Added: 02 Apr 2020 Contributor: PDST Resource type: Exam Papers

SEC past exam question on complex numbers

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Mathematics

Strand: 3. Number

Strand unit: 1. Number Systems (Complex Numbers,Sequences)

Suggestions for use: SEC past exam question to assess understanding of complex numbers

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