Free Lectures Of Math 9th Class Chapter 2: Real and Complex Numbers

Chapter 2: Real and Complex Numbers (94 videos)

Introduction 

      The numbers are the foundation of mathematics and we use different kinds of numbers in our daily life. So it is necessary to be familiar with various kinds of numbers in this unit we shall discuss real numbers and complex numbers including their properties. there is a one-one correspondence between real numbers and the points on the real line. The basic operation of addition, subtraction, multiplication and division on complex numbers will also be discussed in this unit.

Real Numbers

We recall the following sets before giving concepts of real numbers.

Natural Numbers

The numbers 1, 2,3,.... which we use for counting certain objects are called natural numbers or positive integers. The set of natural numbers is denoted by N

i.e.,     N={1,2,3,........}

Whole Numbers

If we include 0 in the set of natural number, the resulting set is the set of whole numbers, denoted by W.   i.e.,       W={0,1,2,3..........}

Integers

The set of integers consists of positive integers. o and negative integers and is denoted by Z i.e.,  

Z={...,-3,-2,-1,0,1,2,3,...}

2.1: Real Numbers
1. Introduction to Real Numbers Introduction to Real Numbers by ADNAN CH
2. Introduction to Rational Numbers Introduction to Rational Numbers by ADNAN CH
3. Problem 1: Introduction to Rational Numbers Problem 1: Introduction to Rational Numbers by ADNAN CH
4. Introduction to Irrational Numbers Introduction to Irrational Numbers by ADNAN CH
5. Problem 1: Introduction to Irrational Numbers Problem 1: Introduction to Irrational Numbers by ADNAN CH
6. Presenting Rational Numbers on Number Line Presenting Rational Numbers on Number Line by ADNAN CH
7. Presenting Irrational Numbers on Number Line Presenting Irrational Numbers on Number Line by ADNAN CH
8. Problem 1: Presenting Irrational Numbers on Number Line Problem 1: Presenting Irrational Numbers on... by ADNAN CH
9. Decimal Representation of Rational Number Decimal Representation of Rational Number by ADNAN CH
10. Problem 1: Decimal Representation of Rational Number Problem 1: Decimal Representation of Rational... by ADNAN CH
11. Decimal Representation of Irrational Number Decimal Representation of Irrational Number by ADNAN CH

2.2: Properties of Real Numbers
1. Closure Law of Rational Numbers Closure Law of Rational Numbers by ADNAN CH
2. Problem 1: Closure Law of Rational Numbers Problem 1: Closure Law of Rational Numbers by ADNAN CH
3. Commutative Law Commutative Law by ADNAN CH
4. Associative Law Associative Law by ADNAN CH
5. Problem 1: Associative Law Problem 1: Associative Law by ADNAN CH
6. Additive Identity & Additive Inverse Additive Identity & Additive Inverse by ADNAN CH
7. Problem 1: Additive Identity & Additive Inverse Problem 1: Additive Identity & Additive Inverse by ADNAN CH
8. Multiplicative Identity & Inverse Multiplicative Identity & Inverse by ADNAN CH
9. Problem 1: Multiplicative Identity & Inverse Problem 1: Multiplicative Identity & Inverse by ADNAN CH
10. Distributive Law Distributive Law by ADNAN CH
11. Problem 1: Distributive Law Problem 1: Distributive Law by ADNAN CH
12. Reflexive And Symmetric Property of Equality Reflexive And Symmetric Property of Equality by ADNAN CH
13. Transitive Property of Equality Transitive Property of Equality by ADNAN CH
14. Problem 1: Transitive Property of Equality Problem 1: Transitive Property of Equality by ADNAN CH
15. Additive Property of Equality Additive Property of Equality by ADNAN CH
16. Multiplicative Property of Equality Cancellation Property of Equality by ADNAN CH Additive Property of Equality by ADNAN CH
17. Cancellation Property of Equality Cancellation Property of Equality by ADNAN CH
18. Problem 1: Cancellation Property of Equality Problem 1: Cancellation Property of Equality by ADNAN CH
19. Trichotomy Property of Inequality Trichotomy Property of Inequality by ADNAN CH
20. Problem 1: Trichotomy Property of Inequality Problem 1: Trichotomy Property of Inequality by ADNAN CH
21. Transitive Property of Inequality Transitive Property of Inequality by ADNAN CH
22. Problem 1: Transitive Property of Inequality Problem 1: Transitive Property of Inequality by ADNAN CH
23. Additive Property of Inequality Additive Property of Inequality by ADNAN CH
24. Multiplicative Property of Inequality Problem 1: Multiplicative Property of Inequality by ADNAN CH
25. Problem 1: Multiplicative Property of Inequality Problem 1: Multiplicative Property of Inequality by ADNAN CH
26. Inequality Multiplicative Inverse Inequality Multiplicative Inverse by ADNAN CH

2.3: Radicals and Radicands
1. Square Root Square Root by ADNAN CH
2. Problem 1: Square Root Problem 1: Square Root by ADNAN CH
3. Properties of Square Root Properties of Square Root by ADNAN CH
4. Problem 1: Properties of Square Root Problem 1: Properties of Square Root by ADNAN CH
5. More on Properties of Square Root More on Properties of Square Root by ADNAN CH
6. qth Root of x qth Root of x by ADNAN CH
7. Problem 1: qth Root of x Problem 1: qth Root of x by ADNAN CH
8. Properties of qth Root of x Properties of qth Root of x by ADNAN CH
9. Problem 1: Properties of qth Root of x Problem 1: Properties of qth Root of x by ADNAN CH
10. Rational Exponents Rational Exponents by ADNAN CH
11. Problem 1: Rational Exponents Problem 1: Rational Exponents by ADNAN CH
12. Properties of Rational Exponents Properties of Rational Exponents by ADNAN CH
13. Problem 1: Properties of Rational Exponents Problem 1: Properties of Rational Exponents by ADNAN CH
14. Proof of x Raise to Power Zero Equals One Proof of x Raise to Power Zero Equals One by ADNAN CH
15. Problem 1: Proof of x Raise to Power Zero Equals One Problem 1: Proof of x Raise to Power Zero... by ADNAN CH
16. Transformation of Radical & Exponential Form Transformation of Radical & Exponential Form by ADNAN CH
17. Problem 1: Transformation of Radical & Exponential Form Problem 1: Transformation of Radical... by ADNAN CH

2.4: Laws of Exponents/Indices
1. Exponent or Index Definition Exponent or Index Definition by ADNAN CH
2. Problem 1: Exponent or Index Definition Problem 1: Exponent or Index Definition by ADNAN CH
3. Law of Sum of Power of Exponents Law of Sum of Power of Exponents by ADNAN CH
4. Problem 1: Law of Sum of Power of Exponents Problem 1: Law of Sum of Power of Exponents by ADNAN CH
5. Law of Power of Product of Exponent Law of Power of Product of Exponent by ADNAN CH
6. Problem 1: Law of Power of Product of Exponent Problem 1: Law of Power of Product of Exponent by ADNAN CH
7. Law of Power of Power of Exponent Law of Power of Power of Exponent by ADNAN CH
8. Problem 1: Law of Power of Power of Exponent Problem 1: Law of Power of Power of Exponent by ADNAN CH
9. Law of Quotient of Power with Same Base Law of Quotient of Power with Same Base by ADNAN CH
10. Problem 1: Law of Quotient of Power with Same Base Problem 1: Law of Quotient of Power with Same Base by ADNAN CH
11. Law of Power of a Fraction Law of Power of a Fraction by ADNAN CH
12. Problem 1: Law of Power of a Fraction Problem 1: Law of Power of a Fraction by ADNAN CH
13. Applications of Laws of Exponents Applications of Laws of Exponents by ADNAN CH
14. Problem 1: Applications of Laws of Exponents Problem 1: Conjugate of Complex Number by ADNAN CH

2.5: Complex Numbers
1. Complex Number Introduction Complex Number Introduction by ADNAN CH
2. Problem 1: Complex Number Introduction Problem 1: Complex Number Introduction by ADNAN CH
3. Definition of Complex Number Definition of Complex Number by ADNAN CH
4. Problem 1: Definition of Complex Number Problem 1: Definition of Complex Number by ADNAN CH
5. Conjugate of Complex Number Problem 1: Definition of Complex Number by ADNAN CH
6. Problem 1: Conjugate of Complex Number Problem 1: Conjugate of Complex Number by ADNAN CH
7. Equality of Complex Number Equality of Complex Number by ADNAN CH
8. Problem 1: Equality of Complex Number Problem 1: Equality of Complex Number by ADNAN CH
9. Properties of Complex Number Properties of Complex Number by ADNAN CH
10. Problem 1: Properties of Complex Number Problem 1: Properties of Complex Number by ADNAN CH
11. Reflexive & Symmetric Law of Complex Number Reflexive & Symmetric Law of Complex Number by ADNAN CH
12. Problem 1: Reflexive & Symmetric Law of Complex Number
13. Transitive Law of Complex Number
14. Problem 1: Transitive Law of Complex Number

2.6: Basic Operations on Complex Numbers
1. Addition of Complex Number Addition of Complex Number by ADNAN CH
2. Problem 1: Addition of Complex Number Problem 1: Addition of Complex Number by ADNAN CH
3. Multiplication of Complex with Scalar Numbers Multiplication of Complex with Scalar Numbers by ADNAN CH
4. Problem 1: Multiplication of Complex with Scalar Numbers Problem 1: Multiplication of Complex with... by ADNAN CH
5. Multiplication of Complex Numbers Multiplication of Complex Numbers by ADNAN CH
6. Problem 1: Multiplication of Complex Numbers Problem 1: Multiplication of Complex Numbers by ADNAN CH
7. Subtraction of Complex Numbers Subtraction of Complex Numbers by ADNAN CH
8. Problem 1: Subtraction of Complex Numbers Problem 1: Subtraction of Complex Numbers by ADNAN CH
9. Division of Complex Numbers Division of Complex Numbers by ADNAN CH
10. Problem 1: Division of Complex Numbers Problem 1: Division of Complex Numbers by ADNAN CH
11. Division Property of Complex Numbers Division Property of Complex Numbers by ADNAN CH
12. Problem 1: Division Property of Complex Numbers Problem 1: Division Property of Complex Numbers by ADNAN CH

free lectures Free Lectures Math 9th free video lectures real and complex numbers

Author: ADNAN CH

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