Chapter 2 - Complex Numbers
This is one of 7 courses which cover the Extension 2 Mathematics Syllabus in NSW.
This set of 7 courses covers the Extension 2 Mathematics Syllabus in NSW.
This is a free course.
Course curriculum
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1
Changes to this content in the 2024 syllabus
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Complex numbers intro
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2
Lesson 1 - Introduction to Complex Numbers
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2024 syllabus changes for this lesson
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How Complex Numbers fit with other Numbers
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Example 1
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Example 1 Video
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Example 2
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Example 2 Video
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Example 3
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Example 3 Video
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Geometric Explanation of i
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Real World Uses of Complex Numbers
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The Complex Plane
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Powers of i
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Example 4
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Example 4 Video
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Example 5
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Example 5 Video
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Exercise 2.1
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Exercise 2.1 Recorded Solutions
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3
Lesson 2 - Cartesian Form
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2024 syllabus changes for this lesson
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Forms of a Complex Number
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Example 1
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Example 1 Video
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Example 2
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Example 2 Video
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Example 3
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Example 3 Video
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Conjugate of a Complex Number
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Example 4
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Example 4 Video
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Example 5
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Example 5 Video
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Example 6
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Example 6 Video
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Example 7
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Example 7 Video
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Exercise 2.2
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Exercise 2.2 Recorded Solutions
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4
Lesson 3 - Mod-arg Form
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2024 syllabus changes for this lesson
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Modulus, Argument and Mod-arg Form
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Example 1
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Example 1 Video
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Example 2
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Example 2 Video
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Multiplying Complex Numbers in Mod-Arg Form
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Example 3
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Example 3 Video
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Division of Complex Numbers in Mod-Arg Form
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Example 4
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Example 4 Video
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Conjugate in Mod-Arg Form
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Example 5
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Example 5 Video
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Exercise 2.3
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Exercise 2.3 Recorded Solutions
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5
Lesson 4 - Exponential Form
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2024 syllabus changes for this lesson
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Exponential Form
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Euler's Formula
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Understanding Exponential Form
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Proving Euler’s Formula
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Proof 1
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Proof 1 Video
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Euler’s Identity
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Proof 2
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Proof 2 Video
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Example 3
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Example 3 Video
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Calculations in Exponential Form
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Example 4
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Example 4 Video
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Example 5
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Example 5 Video
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Exponential Form
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Example 6
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Example 6 Video
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Compare and Convert Between Forms
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Example 7
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Example 7 Video
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Exercise 2.4
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Exercise 2.4 Recorded Solutions
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6
Lesson 5 - Square Roots
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2024 syllabus changes for this lesson
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Method 1 - Simultaneous Equations
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Example 1
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Example 1 Video
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Method 1a - Simultaneous Equations (Shortcut Method)
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Example 2
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Example 2 Video
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Example 3
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Example 3 Video
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Method 2 - Formula
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Example 4
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Example 4 Video
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Example 5
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Example 5 Video
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Exercise 2.5
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Exercise 2.5 Recorded Solutions
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7
Lesson 6 - Conjugate Theorems
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2024 syllabus changes for this lesson
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Product of Conjugates
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Example 1
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Example 1 Video
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Reciprocal of z and its conjugate
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Example 2
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Example 2 Video
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Sum of Conjugates
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Example 3
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Example 3 Video
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Example 4
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Example 4 Video
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Example 5
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Example 5 Video
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Difference of Conjugates
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Example 6
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Example 6 Video
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Example 7
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Example 7 Video
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Operations with Conjugates
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Example 8
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Example 8 Video
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Conjugate Root Theorem
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Example 9
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Example 9 Video
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Exercise 2.6
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Exercise 2.6 Recorded Solutions
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8
Lesson 7 - Complex Numbers as Vectors
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2024 syllabus changes for this lesson
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Complex Numbers as Vectors
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Triangle and Parallelogram Laws (Adding Vectors)
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Subtracting Vectors
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Polygon Law (Adding Vectors)
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Example 1
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Example 1 Video
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Rotation and Dilation
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Parallel Vectors
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Example 2
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Example 2 Video
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Perpendicular Vectors
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Example 3
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Example 3 Video
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Rotating by alpha
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Example 4
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Example 4 Video
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Midpoint
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Example 5
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Example 5 Video
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Triangle Inequality
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Example 6
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Example 6 Video
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Exercise 2.7
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Exercise 2.7 Recorded Solutions
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9
Lesson 8 - Curves and Regions
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2024 syllabus changes for this lesson
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Curves and Regions
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Circles
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Example 1
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Example 1 Video
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Perpendicular Bisector
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Example 2
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Example 2 Video
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Rays and Sectors
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Example 3
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Example 3 Video
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Example 4 (Horizontal and Vertical Lines)
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Example 4 Video
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Example 5 (Algebraic Method)
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Example 5 Video
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Arcs
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Example 6
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Example 6 Video
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Exercise 2.8
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Exercise 2.8 Recorded Solutions
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10
Lesson 9 - De Moivre’s Theorem
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2024 syllabus changes for this lesson
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De Moivre’s Theorem
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Example 1
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Example 1 Video
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Example 2
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Example 2 Video
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Trigonometrical Applications of De Moivre’s Theorem
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Example 3
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Example 3 Video
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Example 4
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Example 4 Video
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Solving Equations with Trigonometric Identities
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Example 5
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Example 5 Video
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Exercise 2.9
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Exercise 2.9 Recorded Solutions
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11
Lesson 10 - Complex Roots
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2024 syllabus changes for this lesson
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Complex Roots of Unity
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Example 1
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Example 1 Video
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Example 2
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Example 2 Video
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Some points to note before we continue
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Example 3
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Example 3 Video
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Complex Roots of -1
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Example 4
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Example 4 Video
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Roots of Other Complex Numbers
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Example 5
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Example 5 Video
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Example 6
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Example 6 Video
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Exercise 2.10
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Exercise 2.10 Recorded Solutions
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Instructor
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.