Master the Fundamentals of Complex Numbers
4.2 (13 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
578 students enrolled

Master the Fundamentals of Complex Numbers

Master the Fundamentals of Complex Numbers
4.2 (13 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
578 students enrolled
Last updated 10/2019
English
English [Auto]
Current price: $44.99 Original price: $64.99 Discount: 31% off
5 hours left at this price!
30-Day Money-Back Guarantee
This course includes
  • 3 hours on-demand video
  • 15 articles
  • 18 downloadable resources
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
Training 5 or more people?

Get your team access to 4,000+ top Udemy courses anytime, anywhere.

Try Udemy for Business
What you'll learn
  • Basic Complex Number Operations
  • Complex Roots of Polynomial Equations
  • Argand Diagrams
  • Modulus-Argument Form (Polar Form) of Complex Numbers
  • Euler's Formula
  • Loci of Complex Numbers (for IGCSE/College-Level)
  • De Moivre's Theorem (for IB/College-Level)
  • Nth Roots of a Complex Number (for IB/College-Level)
  • Problem-Solving involving Complex Numbers
Requirements
  • Be proficient to perform basic operations in indices, algebra, vectors (elementary level) and trigonometry
Description

Dear students,

Welcome to this course "Master the Fundamentals of Complex Numbers"!

This course is designed specially for students who are: doing college-level mathematics, taking their IGCSE/GCE A level or the IB HL Math examinations.

At the end of the course, and depending on which exams you are taking, you will learn most/all of the following:

  • basic complex number operations

  • complex roots of polynomial equations

  • Argand diagrams

  • the modulus-argument form (polar form)

  • multiplication and "division" of complex numbers

  • powers of complex numbers

  • Euler's formula

  • loci of complex numbers (for IGCSE/College-Level)

  • inequalities of complex numbers (for IGCSE/College-Level)

  • De Moivre's Theorem (for IB/College-Level)

  • nth roots of complex numbers (for IB/College-Level)

Along the way, there will be quizzes and practice questions for you to get familiarize with complex numbers. There are also several bonus lectures which will further enhance your understanding of the topic. If you encounter any problems, please do not hesitate to contact me for more clarifications.

I hope that you will find this course useful in your academic pursuit. Enjoy the course! Cheers!


Who this course is for:
  • Students who are taking college-level mathematics
  • Students who are taking the IB HL Mathematics
  • Students who are taking the IGCSE/GCE 'A' level Mathematics
  • Students who need a good foundation in Complex Numbers for University-level modules
Course content
Expand all 48 lectures 03:00:26
+ Introduction to Complex Numbers
3 lectures 08:44

Dear students, a very warm welcome to this introductory course on Complex Numbers! In this course, you will gain valuable insights into the various aspects of Complex Numbers such as the basic operations and Argand Diagrams. Please feel free to watch all the videos and try the practice problems to seek further improvements. Last but not least, do not hesitate to contact me for any clarifications you may need. Thank you and hope you will enjoy the course! ;-)

Preview 04:44

This lecture is to apply what have been taught in the previous lecture to solve the questions in the practice. Try the questions yourself! The solutions will be discussed in the next lecture. Cheers! ;-)

Practice 1
01:08

Solutions to Practice 1. Did you get all the questions correct? ;-D

Practice 1 Answers
02:52
+ Basic Complex Number Operations
3 lectures 20:54

This lecture introduces the various basic number operations of Complex Numbers - addition, subtraction, multiplication etc...

Preview 13:34

This lecture is to apply what have been taught in the previous lecture to solve the questions in the practice. Try the questions yourself! The solutions will be discussed in the next lecture. Cheers! ;-)

Practice 2
01:18

In this lecture, I discuss about the solutions to the practice questions. Did you get all the questions correct? ;-)

Practice 2 Answers
06:02
+ Quiz 1
0 lectures 00:00

This is the first quiz of Complex Numbers. There are a total of 3 questions. Try it! ;-)

Complex Numbers Quiz 1
3 questions
+ Complex Roots of Polynomial Equations
3 lectures 12:07

In this lecture, I introduced the complex roots of polynomial equations and the complex conjugate roots theorem.

Complex Roots of Polynomial Equations
06:32

This lecture is to apply what have been taught in the previous lecture to solve the questions in the practice. Try the questions yourself! The solutions will be discussed in the next lecture. Cheers! ;-)

Practice 3
01:10

This lecture discusses about the solutions to Practice 3 questions. Did you get the answers? ;-)

Practice 3 Answers
04:25
+ Argand Diagrams
3 lectures 16:29

In this lecture, I introduce the Argand diagrams, which are very important graphical representations of Complex Numbers.

Argand Diagrams
09:19

This lecture is to apply what have been taught in the previous lecture to solve the questions in the practice. Try the questions yourself! The solutions will be discussed in the next lecture. Cheers! ;-)

Practice 4
01:33

This lecture discusses about the solutions to the Practice 4 questions. Did you get all of the questions correct? ;-)

Practice 4 Answers
05:37
+ Introduction to the Modulus-Argument Form of Complex Numbers
3 lectures 16:31
The Modulus-Argument Form
10:50
Practice 5
01:31
Practice 5 Answers
04:10
+ Multiplication and Division in Modulus Argument Form
3 lectures 15:37

This lecture discusses about the multiplication and "division" of complex numbers.

Multiplication and Division in Modulus Argument Form
07:30

This lecture is to apply what have been taught in the previous lecture to solve the questions in the practice. Try the questions yourself! The solutions will be discussed in the next lecture. Cheers! ;-)

Practice 6
01:49

It is time to reveal the answers!

Practice 6 Answers
06:18
+ Powers of Complex Numbers
3 lectures 11:55

This lecture introduces the powers of complex numbers and how to handle them.

Powers of Complex Numbers
05:05

This lecture is to apply what have been taught in the previous lecture to solve the questions in the practice. Try the questions yourself! The solutions will be discussed in the next lecture. Cheers! ;-)

Practice 7
01:40

Time to discuss about the answers for the practice questions!

Practice 7 Answers
05:10
+ Introduction to the Euler's Formula
3 lectures 12:42

This lecture introduces the Euler's formula, which presents a very neat and convenient way to represent and manipulate complex numbers.

Euler's Formula
06:59

This lecture is to apply what have been taught in the previous lecture to solve the questions in the practice. Try the questions yourself! The solutions will be discussed in the next lecture. Cheers! ;-)

Practice 8
02:00

In this lecture, let us go through the answers for the practice questions.

Practice 8 Answers
03:43
+ Quiz 2
0 lectures 00:00

This is the second quiz for Complex Numbers. There are a total of 6 questions. Study and try them yourself! ;-)

Complex Numbers Quiz 2
6 questions