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Leaving Certificate Maths: Complex Numbers 6.10.2022

This four-week webinar on Thursday 6th, 13th, 20th & 27th October is suitable for teachers of Leaving Certificate Higher Level Maths and will cover the following:

Session 1
• Number Systems – Natural, Integer, Rational, Real
• Introduction to Imaginary number i
• Complex Numbers, Argand Diagram
• Conjugate of Complex Number
• Modulus of Complex Number
• Addition/Subtraction/Multiplication/Division of Complex Numbers
• Exam Questions
Session 2
• Conjugate Roots Theorem and roots of polynomials
• Solving quadratics with complex roots
• Polar Form
• De Moivre’s Theorem
• Exam Questions
Session 3
• Proof of De Moivre’s Theorem using Induction
• General Polar Form
• Exam Questions
Session 4
• nth roots of unity, n ? N
• identities such as Cos 3? = 4 Cos3 ? – 3 Cos ?
• Transformations using Complex Numbers
• Exam Questions

Note: Typed notes and instructional videos with worked solutions to exam questions will be provided as part of the course material.

Learning Outcomes tied to Leaving Cert Hons Maths Syllabus (Strand 3 & 4)
Strand 3
– recognise irrational numbers and appreciate that R ? Q
– work with irrational numbers
– revisit the operations of addition, multiplication, subtraction and division in the following domains:
• N of natural numbers
• Z of integers
• Q of rational numbers
• R of real numbers and represent these numbers on a number line
– 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
– calculate conjugates of sums and products of complex numbers

Strand 4
– 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 ? + iSin ? )
– use De Moivre’s Theorem
– prove De Moivre’s Theorem by induction for n ? N
– use applications such as nth roots of unity, n

Facilitator: sean Murphy teaching Maths, Physics and Applied Maths to Leaving Cert Honours level for the last twelve years in CBS Ennistymon. I also teach Junior Cycle Science and Coding. I have a website www.hardsums.ie where I share my teaching resources for these subjects with other teachers/students.

From 2012 – 2015, I worked as a local facilitator for the Project Maths Development Team. This involved giving courses for Maths teachers in the Limerick and Clare Education Centres. In the last two years, I have also worked for various Education Centres giving teacher courses in Leaving Cert Honours Maths and Junior Cycle Coding.

In my role as chairman of the Clare/Limerick branch of the IMTA (Irish Maths Teachers’ Association) over the last 5 years I have organised events such as MathsFest 2018 in Limerick (see www.mathsfest.ie)  and TEAM Maths Quizzes for Leaving Cert students. I also maintain the website www.clareimta.ie for sharing resources with maths teachers 

At the national level of the IMTA, I was a member of the subcommittee that worked on the   submission to the NCCA on the new Applied Maths course that is being examined for the first time in 2023. I am also a current member of the IAMTA (Irish Applied Maths Teachers’ Association)

I also give Leaving Cert Honours Maths revision courses every summer for 5th year students going into 6th year at www.mathskillarney.ie  (and formerly at Brú na Páirce, Killarney)

Before changing career to teaching in 2003, I worked as an Electronic Engineer for Parthus/Ceva Inc. ( https://www.ceva-dsp.com ) for 7 years.

Course Properties

Course date 06-10-2022 7:00 pm
Course End Date 27-10-2022 8:00 pm
Cut off date 13-10-2022 4:45 pm
Individual Price Free
Speaker Sean Murphy
Number Hours 4
Location ZOOM online

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