What you'll learn
What are complex numbers
Complex numbers in cartesian form, polar form and exponential form
Complex numbers on the argand diagram
Euler's Formula
Loci of complex numbers
Geometry of complex numbers
Solving polynomial equations involving complex numbers
Finding the nth root
De Moivre's Formula
Requirements
Algebra
Some knowledge of trigonometry, vectors and exponential laws
Description
Welcome to this course on Introduction to Complex Numbers.This course provides a comprehensive introduction to the world of complex numbers, equipping you with the foundational knowledge to confidently solve equations and apply complex numbers in a wide range of fields, including mathematics, engineering, physics, and more.Our course is designed for students who have completed basic algebra and trigonometry. Our curriculum covers everything from algebraic operations with complex numbers to the geometry of the complex plane, polar forms of complex numbers, and the roots of complex numbers. Here's what you will learn:- Complex numbers in different forms (cartesian, polar and exponential form)- Euler's fomula- De Moivre's Formula- Geometry of complex numbers- Conjugates- Loci of complex numbers- Solving n root of complex numbersBy the end of our Introduction to Complex Numbers course, you'll have the confidence and knowledge to apply complex numbers in your work and continue exploring the fascinating world of mathematics. Don't miss out on this opportunity to expand your horizons and enhance your skills. Enroll now!About the InstructorRL Wong is a prolific tutor who had taught many students one-to- one or in group setting in Maths and Sciences. Being a Chemical Engineer for more than a decade, she's familiar with the practical side of Math and Science to the real world, as well, as the concepts behind.
Overview
Section 1: Introduction
Lecture 1 Introduction
Section 2: Introduction to complex numbers
Lecture 2 What are complex numbers?
Lecture 3 The imaginary unit i
Lecture 4 Different powers of i
Section 3: Representing Complex Numbers
Lecture 5 Representing Complex Numbers
Lecture 6 Cartesian form
Lecture 7 Representing Cartesian Form on Argand Diagram
Lecture 8 Polar Form
Lecture 9 Exponential form
Lecture 10 Euler's Formula
Lecture 11 Proving Euler's Formula by Power Series (For your interest)
Lecture 12 Representing Exponential or Polar Form on the Argand Diagram
Lecture 13 More on arg(z) or θ
Section 4: Converting between different forms
Lecture 14 From polar or exponential form to cartesian form
Lecture 15 From cartesian form to polar or exponential form
Section 5: Algebraic operations involving complex numbers
Lecture 16 Operations involving complex numbers
Lecture 17 Addition and Subtraction
Lecture 18 Multiplication with a constant
Lecture 19 Multiplication
Lecture 20 Conjugate
Lecture 21 Rationalize the denominator
Lecture 22 Division
Lecture 23 Division - Cartesian form
Lecture 24 Division - Polar or exponential form
Lecture 25 Power
Section 6: De Moivre's formula
Lecture 26 The Formula
Lecture 27 Proving using laws of exponents and Euler's Formula
Lecture 28 Application of De Moivre's Formula - Part 1
Section 7: Solving equations involving complex roots
Lecture 29 What we will learn
Lecture 30 Solving for real unknowns
Lecture 31 Finding the nth root (exponential form)
Lecture 32 Finding the nth root (polar form)| Application of De Moivre's Formula - Part 2
Lecture 33 Finding the nth root (cartesian form)
Lecture 34 Solving Polynomial equations
Section 8: Argand Diagram and the 4 Operations
Lecture 35 Addition and Subtraction
Lecture 36 Multiplication Part 1
Lecture 37 Multiplication Part 2
Section 9: Complex Loci
Lecture 38 Introduction
Lecture 39 Complex Loci 1
Lecture 40 Complex Loci 2
Lecture 41 Complex Loci 3
Students interested in Complex numbers,Engineering students who are taking math classes,Anyone interested in more advanced Math topics


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