Master The Fundamentals Of Complex Numbers

Master the Fundamentals of Complex Numbers

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 operationscomplex roots of polynomial equationsArgand diagramsthe modulus-argument form (polar form)multiplication and "division" of complex numberspowers of complex numbersEuler's formulaloci 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, PhDoo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo oo

Overview

Section 1: Introduction to Complex Numbers

Lecture 1 Introduction to Complex Numbers

Lecture 2 Practice 1

Lecture 3 Practice 1 Answers

Section 2: Basic Complex Number Operations

Lecture 4 Basic Complex Number Operations

Lecture 5 Practice 2

Lecture 6 Practice 2 Answers

Section 3: Quiz 1

Section 4: Complex Roots of Polynomial Equations

Lecture 7 Complex Roots of Polynomial Equations

Lecture 8 Practice 3

Lecture 9 Practice 3 Answers

Section 5: Argand Diagrams

Lecture 10 Argand Diagrams

Lecture 11 Practice 4

Lecture 12 Practice 4 Answers

Section 6: Introduction to the Modulus-Argument Form of Complex Numbers

Lecture 13 The Modulus-Argument Form

Lecture 14 Practice 5

Lecture 15 Practice 5 Answers

Section 7: Multiplication and Division in Modulus Argument Form

Lecture 16 Multiplication and Division in Modulus Argument Form

Lecture 17 Practice 6

Lecture 18 Practice 6 Answers

Section 8: Powers of Complex Numbers

Lecture 19 Powers of Complex Numbers

Lecture 20 Practice 7

Lecture 21 Practice 7 Answers

Section 9: Introduction to the Euler's Formula

Lecture 22 Euler's Formula

Lecture 23 Practice 8

Lecture 24 Practice 8 Answers

Section 10: Quiz 2

Section 11: Loci of Complex Numbers (for IGCSE/College-Level)

Lecture 25 Loci of Complex Numbers and Locus of a Circle

Lecture 26 Practice 9

Lecture 27 Practice 9 Answers

Lecture 28 Locus of a Perpendicular Bisector

Lecture 29 Practice 10

Lecture 30 Practice 10 Answers

Lecture 31 Locus of a Half-line

Lecture 32 Practice 11

Lecture 33 Practice 11 Answers

Section 12: Inequalities in Complex Numbers (for IGCSE/College-Level)

Lecture 34 Inequalities in Complex Numbers

Lecture 35 Practice 12

Lecture 36 Practice 12 Answers

Section 13: De Moivre's Theorem (for IB HL/College-Level)

Lecture 37 De Moivre's Theorem

Lecture 38 Practice 13

Lecture 39 Practice 13 Answers

Section 14: Nth Roots of a Complex Number (for IB HL/College-Level)

Lecture 40 Nth Roots of a Complex Number

Lecture 41 Practice 14

Lecture 42 Practice 14 Answers

Section 15: Quiz 3

Section 16: Bonus! Problem-Solving Exercises, Solutions to Quizzes and an Extra Video!

Lecture 43 Complex Numbers Problem-Solving Exercises

Lecture 44 Answers to Problem-Solving Exercises

Lecture 45 Bonus! Correction of Argument to Principal Value

Lecture 46 Written Solutions to the Quizzes

Lecture 47 Further Problem-Solving Exercise 1

Lecture 48 Lecture 48: Further Problem-Solving Exercise 2

Section 17: Summary and Conclusions

Lecture 49 Summary and Conclusions

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