Complex Numbers (Part-1)

21 students enrolled

An introductory guide for mastering basic concepts of Complex Numbers.

21 students enrolled

Created by
Surya Kumari Gandikota

Last updated 3/2017

English

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.

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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