Published 3/2023MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHzLanguage: English | Size: 1.03 GB | Duration: 4h 10m

Complex numbers in cartesian, polar and exponential form| Euler's and De Moivre's formula| Loci & Geometry| Solve roots

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, eeering, 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 Chal Eeer 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,Eeering students who are taking math classes,Anyone interested in more advanced Math topics

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