Course Description

This course provides teachers with a comprehensive guide to the knowledge and techniques required to teach the new NSW Mathematics Extension 2 syllabus. 

The course goes into greater detail than the textbooks, so teachers are more comfortable in their ability to deliver the content. All 124 examples have been recorded, so that you can watch an experienced maths teacher talk through the examples and any important points to note.

Ext2#2 covers Complex Numbers (MEX-N1 and MEX-N2), a topic that is usually taught early in the course.

New and existing content is explored in detail, including interesting and more efficient techniques that experienced teachers may not have seen before. Important points to be covered with students are noted, and the limits of the syllabus are discussed. As more detail on the syllabus is released by NESA any changes required will be made. Also included are related skills that are beyond the syllabus that you can use to extend more capable students.

The course includes:

  • 124 recorded examples

  • 217 page course handout

  • 124 optional practice questions matching the examples from the course, with fully worked solutions

A suggested scope and sequence for Year 12 Advanced, Extension 1 and Extension 2 for combined classes is provided, plus a lesson by lesson breakdown of the Advanced, Extension 1 and Extension 2 courses for Year 11 and 12 to help you create your own scope and sequences.


Mathematics teachers who are preparing to teach the new Extension 2 syllabus. This course is suitable for teachers with any level of previous experience.

Teaching Standards

2.1.2 Proficient Level - Know the content and how to teach it - Content and teaching strategies of the teaching area:  Apply knowledge of the content and teaching strategies of the teaching area to develop engaging teaching activities

Do you teach in NSW? If so, this is relevant to you:

Completing Mathematics Extension 2: Complex Numbers - EXT2#2 will contribute 10 hours of NSW Education Standards Authority (NESA) Accredited PD in the priority area of Delivery and assessment of NSW Curriculum/Early Years Learning Framework addressing standard descriptors 2.1.2 from the Australian Professional Standards for Teachers towards maintaining Proficient Teacher Accreditation in NSW.


Course curriculum

  • 1


    • Course Administration

    • Introduction to the Mathematics Extension 2 In Depth Year 12 Series

    • Introduction to Part II

  • 2

    Complex Numbers

    • Introduction to Complex Numbers

  • 3

    Complex Numbers 1 - Introduction to Complex Numbers

    • Lesson Overview

    • How Complex Numbers fit with other Number Systems

    • Imaginary Numbers

    • Definition of 𝑖

    • Geometric Explanation of 𝑖

    • Now Isn’t 𝑖 the Square Root of -1?

    • Surd Laws

    • Real World Uses of Complex Numbers

    • The Complex Plane

    • Powers of 𝑖

    • Powers of −1

    • Lesson 1 Quiz

  • 4

    Complex Numbers 2 - Cartesian Form

    • Lesson Overview

    • Forms of a Complex Number

    • Calculations in Cartesian Form

    • Addition and Subtraction

    • Multiplication

    • Squaring and Powers

    • Conjugates and Division

    • Equal Complex Numbers

    • Combining Operations

    • Lesson 2 Quiz

  • 5

    Complex Numbers 3 - Polar Form

    • Lesson Overview

    • Modulus, Argument and Polar Form

    • Multiplying Complex Numbers in Polar Form

    • Division of Complex Numbers in Polar Form

    • Conjugate in Polar Form

    • Converting Rectangular to/from Polar Form

    • Lesson 3 Quiz

  • 6

    Complex Numbers 4 - Exponential Form

    • Lesson Overview

    • Exponential Form

    • Explaining Exponential Form and Euler’s Formula

    • Proving Euler’s Formula

    • Euler’s Identity

    • Calculations in Exponential Form

    • Compare and Convert Between Forms

    • Lesson 4 Quiz

  • 7

    Complex Numbers 5 - Square Roots

    • Lesson 5 Overview

    • Square Roots Using Simultaneous Equations

    • Square Roots Using Formula

    • Lesson 5 Quiz

  • 8

    Complex Numbers 6 - Conjugate Theorems

    • Lesson Overview

    • Conjugate Proofs

    • Conjugate Root Theorem

    • Lesson 6 Quiz

  • 9

    Complex Numbers 7 - Complex Numbers as Vectors

    • Lesson Overview

    • Complex Numbers as Vectors

    • Translations

    • Rotation and Dilation

    • Midpoint

    • Triangle Inequality

    • Lesson 7 Quiz

  • 10

    Complex Numbers 8 - Curves and Regions

    • Lesson Overview

    • Circles

    • Perpendicular Bisector

    • Rays and Sectors

    • Horizontal and Vertical Lines

    • Hyperbolas

    • Algebraic Method

    • Arcs

    • Lesson 8 Quiz

  • 11

    Complex Numbers 9 - de Moivre's Theorem

    • Lesson Overview

    • De Moivre’s Theorem

    • Trigonometrical Applications of De Moivre’s Theorem

    • Lesson 9 Quiz

  • 12

    Complex Numbers 10 - Complex Roots

    • Lesson Overview

    • Complex Roots of Unity

    • Complex Roots of −1

    • Roots of Other Complex Numbers

    • Lesson 10 Quiz

  • 13


    • Highlights of Complex Numbers

    • Conclusion to Part II

  • 14

    Course Feedback

    • Course Feedback

Presented by Steve Howard

Steve Howard

Steve Howard

Steve Howard has inspired and equipped hundreds of Maths teachers with his In-Depth Senior Mathematics courses, providing all the tips, examples and resources to teach the HSC syllabus with confidence. He loves to discover the most efficient techniques for solving mathematical problems, by analysing other experts' solutions or by developing his own approaches when he finds a better way. As a student, Steve did Unit 4 Mathematics, gaining a mark of 198/200, before training as an actuary. After retraining as a teacher, Steve has taught Maths at Cowra High School, NSW, for 28 years. He has also taught gifted and talented students online through Xsel and Aurora College, and developed all student course material for TTA's Year 12 Extension Maths Portal.

Other Courses by Steve Howard

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