Complex Numbers (As-A Level-Ib-Igcse-College Level)

Complex Numbers from Basics to Advanced

What you’ll learn
Iota, Imaginary Numbers, Properties of Iota
Complex Numbers, Algebra of Complex Numbers, Square Root of Complex Number
Complex Roots of Quadratic, Cubic & Quartic Equations
Argand Diagrams, Vector Form, Representation of Complex Number
Modulus & Argument of a Complex Number
Modulus-Argument Form, Polar Form, Exponential Form of Complex Number
Properties of Argument and Modulus of Multiplication & Division
Loci (Circle, Perpendicular Bisector, A Ray)
Covered questions on all the concepts in each video

Requirements
Basic Algebra
Vectors
Coordinate Geometry

Description
Welcome to world of Imaginary NumbersComplex Numbers is one of the most important and most interesting topics from algebra. In this course you will have in depth knowledge of complex numbers from basics to advanced.Concepts covered:1. Introduction of complex numbers2. Algebra of Complex Numbers3. Argand Diagrams4. Modulus and Argument 5. Using Vectors in adding and subtracting6. Quadratic, Cubic, Quartic equations with complex roots7. Different ways to represent complex numbers (Modulus Argument form, Euler`s Form, Polar Form) 8. Loci in Argand DiagramsEvery topic & concept is covered in detail and with good number of problems.Prerequisites:Though this course covers complex number from basic to advanced but a student should know following topics:1. Basic Algebra2. Basics of Vectors3. Basics of TrigonometryThe course flow is designed such that you will get so involved in the topic. The flow is from basic to advance level. Even if you are good with this concept, you will definitely find something new & interesting. The instructor has carefully selected problems you will definitely enjoy solving. It is recommended that you watch videos in the same sequence as given for better understanding and correlation. A large set of problems are solved for thorough understanding of the concepts.The instructor is very experienced to understand the problems faced by students. With the vast teaching experience at different levels, the instructor has chosen flow, the topics and problems to make you understand the complex numbers in best of the method. This course is among the most exhaustive courses on Complex Numbers available.Keep Learning, Have fun with Complex Numbers.Enjoy the course.

Overview
Section 1: Introduction

Lecture 1 Why we need imaginary numbers

Lecture 2 Introduction of square root (-1) that is IOTA

Lecture 3 Powers of i

Lecture 4 Introduction of Complex Numbers

Lecture 5 Algebra of Complex Numbers – (Add, Subtract and Multiply)

Lecture 6 Algebra of Complex Nos (Division of two complex numbers)

Lecture 7 Questions based on Algebra of Complex Numbers

Lecture 8 Square Root of C. No

Lecture 9 Quadratic Equation with Complex Roots

Lecture 10 Cubic & Quartic Equations having complex roots

Lecture 11 Questions based on Quadratic/Cubic/Quartic Equations having complex roots

Section 2: Geometry of Complex Numbers

Lecture 12 Argand Diagrams

Lecture 13 Modulus of Complex Numbers

Lecture 14 Argument of Complex Numbers

Lecture 15 Using Vectors for Adding and Subtracting complex numbers

Lecture 16 Different Forms of Complex Numbers

Lecture 17 Argument & Modulus of multiplication and division

Section 3: Loci on Argand Diagram

Lecture 18 Perpendicular Bisectors

Lecture 19 Circle on Argand Diagram

Lecture 20 Interesting Question on Locus

Lecture 21 Loci related to Argument (A Ray)

Lecture 22 Regions in Argand Diagram -1

Lecture 23 Regions in Argand Diagram -2

Lecture 24 Regions in Argand Diagram – 3

Lecture 25 Interesting Question on Regions

AS/A Level,Pure Mathematics,O Level/A level