Complex Numbers

This online course is developed to cover all the content required for HSC Mathematics Extension 2 students studying Complex Numbers.

We will cover arithmetic of complex numbers, the Argand diagram, polar form of complex numbers, properties of complex conjugates, vectors with complex numbers, locus, de Moivre’s theorem and applications, roots of unity, and polynomials with complex numbers.

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Meet Huan

- -

Meet Huan - -

Hello! I am Huan - founder of EIM Tuition.

Growing up in a first-generation immigrant family, I experienced first-hand the belief that education is the key to opportunity. Like many of the students I have helped, I went through the grind of preparing for the HSC, aiming for a top ATAR in a highly competitive selective high school environment.

That journey shaped how I teach (and EIM operates) today. Since 2010, I’ve helped 1,000+ students from 50+ schools across Sydney achieve outstanding results - including 99.95 ATARs, state ranks and countless Band 6’s.

Through these online courses, I hope to share the same clarity, structure and strategies that have helped so many students succeed - and help you achieve your own goals, wherever you’re studying from.

Course FAQ

Stay tuned!

1. Introduction to Complex Numbers

2. Example 1

3. Example 2

4. Example 3

5. Example 4

6. Example 5

7. Example 6

1. Example 7

2. Example 8

3. Example 9

4. Example 10

1. Example 11

2. Example 12

3. Example 13

4. Example 14

1. The Argand Diagram + Example 1

2. Example 2

1. Modulus and Argument

2. Example 3

3. Example 4

4. Example 5

5. Example 6

6. Example 7

1. Multiplication and Division of Complex Numbers using Trigonometry

2. Example 8

3. Example 9

4. Example 10

5. Example 11

6. Example 12

7. Example 13

8. Example 14

9. Example 15

1. Exponential Form

2. Example 16

3. Example 17

4. Example 18

5. Example 19

6. Exponential Form Extended

7. Example 20

8. Multiplication and Division of Complex Numbers in Exponential Form

9. Example 21

10. Example 22

11. Example 23

1. Properties of Complex Conjugates

2. Example 24

3. Example 25

4. Example 26

5. Example 27

6. Example 28

7. Example 29

1. Representing Vectors using Complex Numbers

1. Vector Addition

2. Example 1

3. Example 2

4. Example 3

5. Example 4

1. Rotation and Dilation of Vectors

2. Example 5

3. Example 6

4. Example 7

5. Example 8

6. Example 9

7. Example 10

8. Example 11

9. Example 12

10. Example 13

1. Angle Difference between Two Vectors

2. Example 14

3. Example 15

4. Example 16

1. Triangular Inequalities

2. Example 18

3. Example 19

4. Example 20

1. Locus: Length Constraint

2. Example 1

3. Example 2

4. Example 3

5. Example 4

6. Example 5