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Chapter 2: Real and Complex Number Systems (143 videos)

2.1: Introduction
1. Introduction to Real Numbers
2. Problem-Introduction to Real Numbers
3. Depiction of Real Number on Number Line
 
2.2: Development of Number Systems
1. Negative Numbers
2. Integers
3. Introduction to Rational Numbers
4. Problem 1: Introduction to Rational Numbers
5. Introduction to Irrational Numbers
6. Problem 1: Introduction to Irrational Numbers
7. Introduction to Real Numbers
8. Problem-Introduction to Real Numbers
 
2.3: Distinction of Between Rational and Irrational Numbers
1. Presenting Rational Numbers on Number Line
2. Problem-Decimal Representation of Rational Number
3. Presenting Irrational Numbers on Number Line
4. Problem-Decimal Representation of Irrational Number
5. Problem 1: Presenting Irrational Numbers on Number Line
6. Proving Square Root of Prime Number is Irrational Number
7. Problem-Proving Square Root of Prime Number is Irrational Number
 
2.4: The Real Number System
1. Closure law of Whole Numbers Addition and Multiplication
2. Closure law of Whole Numbers Subtraction and Division
3. Closure law of Integers Addition, Multiplication & Subtraction
4. Closure law of Integers Division
5. Problem 1: Closure law of Integers Addition, Multiplication & Subtrac
6. Closure Law of Rational Numbers
7. Closure law of Rational Numbers Subtraction and Division
8. Problem-Closure Law of Rational Numbers
9. Problem 1: Closure Law of Rational Numbers
10. Closure law of Irrational Numbers Addition and Subtraction
11. Closure law of Irrational Numbers Multiplication and Division
12. Commutative Law
13. Commutative law under Subtration and Division
14. Problem-Commutative Law
15. Associative Law
16. Associative law of Subtraction and Division
17. Problem-Associative Law
18. Problem 1: Associative Law
19. Additive Identity & Additive Inverse
20. Problem-Additive Identity & Additive Inverse
21. Problem 1: Additive Identity & Additive Inverse
22. Multiplicative Identity & Inverse
23. Problem-Multiplicative Identity & Inverse
24. Problem 1: Multiplicative Identity & Inverse
25. Distributive Law
26. Distributive Property of Multiplication over Subtraction
27. Problem-Distributive Law
28. Problem 1: Distributive Law
29. Problem 1: Distributive law of Multiplication over Subtraction
30. Trichotomy Property of Inequality
31. Problem-Trichotomy Property of Inequality
32. Problem 1: Trichotomy Property of Inequality
33. Reflexive And Symmetric Property of Equality
34. Problem-Reflexive And Symmetric Property of Equality
35. Transitive Property of Equality
36. Problem-Transitive Property of Equality
37. Problem 1: Transitive Property of Equality
38. Additive Property of Equality
39. Problem-Additive Property of Equality
40. Multiplicative Property of Equality
41. Problem-Multiplicative Property of Equality
42. Cancellation Property of Equality
43. Problem-Cancellation Property of Equality
44. Problem 1: Cancellation Property of Equality
45. Density Property
46. Problem-Density Property
47. Archimedian Property of Inequality
48. Problem-Transitive Property of Inequality
49. Problem 1: Transitive Property of Inequality
50. Additive Property of Inequality
51. Problem-Additive Property of Inequality
52. Multiplicative Property of Inequality
53. Problem 1: Multiplicative Property of Inequality
54. Inequality Multiplicative Inverse
55. Problem-Inequality Multiplicative Inverse
56. Indeterminate Form
57. Golden Rule of Fractions
58. Principle of Equality of Fractions
59. Rule for Quotient of Fractrions
 
2.5: The System C of Complex Numbers
1. Complex Number Introduction
2. Problem-Complex Number Introduction
3. Problem 1: Complex Number Introduction
4. Definition of Complex Number
5. Problem 1: Definition of Complex Number
6. Problem-Definition of Complex Number
7. Equality of Complex Number
8. Problem 1: Equality of Complex Number
9. Problem-Equality of Complex Number
10. Addition of Complex Number
11. Problem 1: Addition of Complex Number
12. Problem-Addition of Complex Number
13. Multiplication of Complex with Scalar Numbers
14. Problem 1: Multiplication of Complex with Scalar Numbers
15. Problem-Scalar Multiplication of Complex Numbers
16. Multiplication of Complex Numbers
17. Problem 1: Multiplication of Complex Numbers
18. Problem-Multiplication of Complex Numbers
 
2.6: Properties of Complex Numbers
1. Commutative Property of Complex Numbers
2. Problem-Commutative Property of Complex Numbers
3. Associative Property of Complex Numbers
4. Problem-Associative Property of Complex Numbers
5. The Distributive Property of Complex Numbers
6. Problem-The Distributive Property of Complex Numbers
7. Additive Identity and Multiplicative Identity of Complex Numbers
8. Problem-Additive Identity and Multiplicative Identity of Complex Numb
9. Additive Inverse and Multiplicative Inverse of Complex Numbers
10. Problem-Additive Inverse and Multiplicative Inverse of Complex Numbers
11. Solution of Simultaneous Linear Equations with Complex Co-efficients
12. Problem-Solution of Simultaneous Linear Equations with Complex Co-eff
13. Expression of the Polynomial P ( z ) as a Product of Linear Factors
14. Problem-Expression of the Polynomial P ( z ) as a Product of Linear F
15. Quadratic Equation of Complex Variables
16. Problem-Quadratic Equation of Complex Variables
 
2.7: Definition of Imaginary Numbers
1. Complex Numbers as Ordered Pairs of Real Numbers
2. Problem 1: Definition of Complex Number
 
2.8: Conjugate of Complex Numbers
1. Conjugate of Complex Number
2. Problem 1: Conjugate of Complex Number
3. Problem 2: Conjugate of Complex Number
4. Problem-Conjugate of Complex Number
 
2.9: Modulus of a Complex Number
1. Modulus of Complex Number
2. Problem-Modulus of Complex Number
3. Theorems on Complex Number
4. More on Theorems on Complex Numbers
5. Problem-Theorems on Complex Number
 
2.10: The Subtraction of Complex Numbers
1. Subtraction of Complex Numbers
2. Problem 1: Subtraction of Complex Numbers
3. Problem-Subtraction of Complex Numbers
 
2.11: The Division of Complex Numbers
1. Division of Complex Numbers
2. Problem 1: Division of Complex Numbers
3. Problem-Division of Complex Numbers
4. Division Property of Complex Numbers
5. Problem 1: Division Property of Complex Numbers
6. Problem-Division Property of Complex Numbers
 
2.12: Geometrical Representation of the Complex Number x + iy as Pair of Real Numbers
1. Argand Diagram
2. Problem-Argand Diagram
3. Modulus of Complex Number
4. Problem-Modulus of Complex Number
 
2.13: The Order Relations
1. The Order Relations
2. Problem-The Order Relations
 
2.14: Vector Interpretation of Complex Numbers
1. Vector Interpretation of Complex Numbers
2. Problem-Vector Interpretation of Complex Numbers
 
2.15: The Triangle Inequality
1. The Triangle Inequality
2. Problem-The Triangle Inequality
 
2.16: Real and Imaginary Parts of ( x + iy ) Power n
1. Real and Imaginary parts of Expression of Power n
2. Problem-Real and Imaginary parts of Expression of Power n
 

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