Master the Fundamentals of Complex Numbers

Highest Rated

Created byDr Ling Meng Kay Daniel, PhD

Last updated 12/2021

English

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

Course content

17 sections • 49 lectures • 3h 4m total length

Introduction to Complex Numbers4:44
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! ;-)
Practice 11:08
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 Answers2:52
Solutions to Practice 1. Did you get all the questions correct? ;-D

Basic Complex Number Operations13:34
This lecture introduces the various basic number operations of Complex Numbers - addition, subtraction, multiplication etc...
Practice 21:18
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 Answers6:02
In this lecture, I discuss about the solutions to the practice questions. Did you get all the questions correct? ;-)

Complex Roots of Polynomial Equations6:32
In this lecture, I introduced the complex roots of polynomial equations and the complex conjugate roots theorem.
Practice 31:10
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 Answers4:25
This lecture discusses about the solutions to Practice 3 questions. Did you get the answers? ;-)

Argand Diagrams9:19
In this lecture, I introduce the Argand diagrams, which are very important graphical representations of Complex Numbers.
Practice 41:33
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 Answers5:37
This lecture discusses about the solutions to the Practice 4 questions. Did you get all of the questions correct? ;-)

Multiplication and Division in Modulus Argument Form7:30
This lecture discusses about the multiplication and "division" of complex numbers.
Practice 61:49
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 Answers6:18
It is time to reveal the answers!

Powers of Complex Numbers5:05
This lecture introduces the powers of complex numbers and how to handle them.
Practice 71:40
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 Answers5:10
Time to discuss about the answers for the practice questions!

Euler's Formula6:59
This lecture introduces the Euler's formula, which presents a very neat and convenient way to represent and manipulate complex numbers.
Practice 82:00
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 Answers3:43
In this lecture, let us go through the answers for the practice questions.

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 familiarized 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!

Dr Ling M K Daniel, PhD

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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

Master the Fundamentals of Complex Numbers

What you'll learn

Explore related topics

Course content

Introduction to Complex Numbers3 lectures • 9min

Basic Complex Number Operations3 lectures • 21min

Quiz 10

Complex Roots of Polynomial Equations3 lectures • 12min

Argand Diagrams3 lectures • 16min

Introduction to the Modulus-Argument Form of Complex Numbers3 lectures • 17min

Multiplication and Division in Modulus Argument Form3 lectures • 16min

Powers of Complex Numbers3 lectures • 12min

Introduction to the Euler's Formula3 lectures • 13min

Quiz 20

Requirements

Description

Who this course is for: