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Complex Numbers (Part-1)

An introductory guide for mastering basic concepts of Complex Numbers.
5.0 (2 ratings)
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18 students enrolled
Last updated 4/2015
English
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Includes:
  • 1 hour on-demand video
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
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What Will I Learn?
understand the need for complex numbers and define imaginary numbers.
know how the real number system is extended to the complex number system.
become familiar with the term iota (i), the notation for imaginary numbers.
understand the definition of positive and negative integral powers of i (iota)
define the following terms: 1. Complex number 2. Real part of a complex number 3. Imaginary part of a complex number with the help of examples.
encounter problems based on integral powers of i (iota).
define the following terms: purely real and purely imaginary complex numbers
understand the equality of two complex numbers and the operation addition of complex numbers.
establish the laws of addition. i.e. Closure law, commutativity, associativity , existence of additive identity and inverse.
take a quiz at the beginning of the course which will serve as a self assessment tool for students to see how much do they know about real numbers before they start learning complex numbers.
View Curriculum
Requirements
  • To take this course you must be familiar with the real number system. i.e. the natural numbers, whole numbers, integers, rational and irrational numbers.
  • Also you must have knowledge of operations of addition, subtraction, multiplication and division of real numbers.
  • You must also know the following properties or laws of real numbers: Closure, Commutativity, Associativity, Distributivity and the identity and inverse elements for addition and multiplication.
Description

This course is for K-11 and K-12 grade students, who want an introduction to the topic,"Complex numbers".

The course begins with a quiz which will serve as a self assessment tool for students to see how much do they know about real numbers before they start learning complex numbers.

The first lecture presents a clear understanding of the need for complex numbers and define imaginary numbers.

And hence the students get to know how the real number system is extended to the complex number system.

The students will be introduced to the term iota (i), the notation for imaginary numbers.

The definitions of positive and negative integral powers of i (iota) are very clearly explained.

Appropriate examples to understand the powers of iota are taken up.

The terms: Complex numbers, Real part of a complex number, Imaginary part of a complex number, purely real and purely imaginary complex numbers are explained with the help of examples.

Two of the lectures explain the equality of two complex numbers and the operation addition of complex numbers.

Section 4 comprises of videos which establish the laws of addition. i.e. Closure law, commutativity, associativity , existence of additive identity and inverse.

The quizzes in the course help the students to test their understanding.

The videos can be completed in an hour.

This course of Complex numbers (part 1) is sure to make understand your concepts easily and this will serve as a great foundation for other advanced courses in complex numbers which you may want to take up in the future.

Good Luck!

Who is the target audience?
  • The lectures in this course will be helpful to K-11 and K-12 grade students, who want an introduction to the topic,"Complex numbers".
  • Other than K-11 and K-12 grade students, this course will help the students of high school and who are studying Algebra-2 or those who are doing an advance course in Mathematics and want to review the topic complex numbers.
  • This course is a bonus for people who have keen interest in the subject of Mathematics and also for the people who have great passion for the subject!
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Curriculum For This Course
Expand All 13 Lectures Collapse All 13 Lectures 52:13
+
Review of Concepts.
0 Lectures 00:00

This quiz will be a self assessment for students to see how much do they know about real numbers before they learn complex numbers.

Review of Concepts.
10 questions
+
Introduction to imaginary numbers
4 Lectures 30:02

In this video you will understand the need for complex numbers and define imaginary numbers.

Preview 06:34

In this video you will understand the definition of positive integral powers of i (iota).

Preview 04:17

In this lecture we shall define the negative powers of i (iota).

Negative integral powers of i (iota).
04:49

In this video we shall discuss examples on powers of iota.

Examples on powers of i (iota).
14:22

Multiple choice type
3 questions
+
Definition of a complex number
3 Lectures 06:42

In this lecture we shall define the following terms:

1. Complex number 2. Real part of a complex number 3. Imaginary part of a complex number

Definition of a Complex number.
02:48

Multiple choice type
2 questions

In this video students shall understand the terms purely real and purely imaginary complex numbers.

Purely real and purely imaginary complex numbers.
02:02

In this lecture we shall discuss when two complex numbers are said to be equal.

Equality of two complex numbers
01:52
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Addition of complex numbers.
6 Lectures 15:29

Will be able to define the mathematical operation addition on complex numbers.

Addition of complex numbers
02:26

In this lecture we shall prove that the set of complex numbers is closed under addition.

Closure law for addition
01:52

In this video the commutative law for addition of complex numbers is discussed.

Commutative law for addition
01:43

In this video the associativity law for addition of complex numbers is discussed.

Associative law for addition
03:21

In this video the existence of additive identity will be proved.

Existence of Additive Identity
02:25

In this lecture the existence of aditive inverse is discussed.

Existence of additive inverse
03:42
About the Instructor
4.4 Average rating
57 Reviews
4,067 Students
5 Courses

I am Mathematics Subject Matter Expert.

I am a certified (post graduate trained) mathematics instructor (private tutor) with over 24 years of teaching experience to middle school, high school, senior secondary level and intermediate level covering various school boards including CBSE, ICSE, ISC, IGCSE, 2-year IB Diploma (International Baccalaureate) covering AL,SL and HL courses. I have so far made 200+ videos in various Math topics.

Worked for:

FIITJEE EDU SOFT Ltd. as

CHIEF CONTENT MODERATOR under the department of

SYSTEM DEVELOPMENT associated with the project

EDFORA (Education for All) in Gurgaon.

Key Responsibilities held: 1. Overall content direction ( in making educational videos).

2. Managing quality of content created by content contributors.

3. Refining checklist and checklist of content.

4. Leading the team of HODs and Domain Auditors.

5. Creating training collateral for content creators.

6. Establish QA/QC Benchmarks for Videos

7. Work closely with HODs to achieve domain wise targets and drive the process from Review to Publish

8 .Providing overall guidance/ direction to the content team for preparing content for different state boards.[ CBSE, ICSE, ISC, Andhra Pradesh Board, Madhya Pradesh Board, Maharashtra Board, Rajasthan Board, Uttar Pradesh Board]

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