Complex Numbers (Part-1)
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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.
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|Section 1: Review of Concepts.|
|Quiz 1||10 questions|
This quiz will be a self assessment for students to see how much do they know about real numbers before they learn complex numbers.
|Section 2: Introduction to imaginary numbers|
In this video you will understand the need for complex numbers and define imaginary numbers.
In this video you will understand the definition of positive integral powers of i (iota).
In this lecture we shall define the negative powers of i (iota).
In this video we shall discuss examples on powers of iota.
Multiple choice type
|Section 3: Definition of a complex number|
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
Multiple choice type
In this video students shall understand the terms purely real and purely imaginary complex numbers.
In this lecture we shall discuss when two complex numbers are said to be equal.
|Section 4: Addition of complex numbers.|
Will be able to define the mathematical operation addition on complex numbers.
In this lecture we shall prove that the set of complex numbers is closed under addition.
In this video the commutative law for addition of complex numbers is discussed.
In this video the associativity law for addition of complex numbers is discussed.
In this video the existence of additive identity will be proved.
In this lecture the existence of aditive inverse is discussed.
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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.
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