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Chapter 1: Numbers System (147 videos)

1.1: Introduction
1. Problem-Introduction to Real Numbers
2. Introduction to Real Numbers
 
1.2: Rational Numbers and Irrational Numbers
1. Presenting Rational Numbers on Number Line
2. Problem-Decimal Representation of Rational Number
3. Problem-Proving Square Root of Prime Number is Irrational Number
4. Presenting Irrational Numbers on Number Line
5. Problem-Decimal Representation of Irrational Number
6. Proving Square Root of Prime Number is Irrational Number
7. Problem 1: Presenting Irrational Numbers on Number Line
 
1.3: Properties of Real Numbers
1. Closure Law of Rational Numbers
2. Closure law of Rational Numbers Subtraction and Division
3. Problem-Closure Law of Rational Numbers
4. Associative Law
5. Problem 1: Closure Law of Rational Numbers
6. Commutative Law
7. Additive Identity & Additive Inverse
8. Multiplicative Identity & Inverse
9. Commutative law under Subtration and Division
10. Distributive Law
11. Problem-Commutative Law
12. Reflexive And Symmetric Property of Equality
13. Transitive Property of Equality
14. Associative law of Subtraction and Division
15. Additive Property of Equality
16. Problem 1: Associative Law
17. Problem-Associative Law
18. Multiplicative Property of Equality
19. Cancellation Property of Equality
20. Trichotomy Property of Inequality
21. Problem-Additive Identity & Additive Inverse
22. Transitive Property of Inequality
23. Problem 1: Additive Identity & Additive Inverse
24. Additive Property of Inequality
25. Multiplicative Property of Inequality
26. Problem-Multiplicative Identity & Inverse
27. Inequality Multiplicative Inverse
28. Problem 1: Multiplicative Identity & Inverse
29. Indeterminate Form
30. Golden Rule of Fractions
31. Distributive Property of Multiplication over Subtraction
32. Principle of Equality of Fractions
33. Problem-Distributive Law
34. Rule for Quotient of Fractrions
35. Problem 1: Distributive Law
36. Problem 1: Distributive law of Multiplication over Subtraction
37. Problem-Trichotomy Property of Inequality
38. Problem 1: Trichotomy Property of Inequality
39. Problem-Reflexive And Symmetric Property of Equality
40. Problem-Transitive Property of Equality
41. Problem 1: Transitive Property of Equality
42. Problem-Additive Property of Equality
43. Problem-Multiplicative Property of Equality
44. Problem-Cancellation Property of Equality
45. Problem 1: Cancellation Property of Equality
46. Density Property
47. Problem-Density Property
48. Archimedian Property of Inequality
49. Problem-Transitive Property of Inequality
50. Problem 1: Transitive Property of Inequality
51. Problem-Additive Property of Inequality
52. Problem 1: Multiplicative Property of Inequality
53. Problem-Inequality Multiplicative Inverse
 
1.4: Complex Numbers
1. Complex Number Introduction
2. Problem-Complex Number Introduction
3. Definition of Complex Number
4. Conjugate of Complex Number
5. Problem 1: Complex Number Introduction
6. Equality of Complex Number
7. Properties of Complex Number
8. Problem 1: Definition of Complex Number
9. Problem-Definition of Complex Number
10. Reflexive & Symmetric Law of Complex Number
11. Transitive Law of Complex Number
12. Addition of Complex Number
13. Problem 1: Conjugate of Complex Number
14. Multiplication of Complex with Scalar Numbers
15. Problem 2: Conjugate of Complex Number
16. Problem-Conjugate of Complex Number
17. Multiplication of Complex Numbers
18. Problem 1: Reflexive & Symmetric Law of Complex Number
19. Subtraction of Complex Numbers
20. Solution of Simultaneous Linear Equations with Complex Co-efficients
21. Problem-Reflexive & Symmetric Law of Complex Number
22. Division of Complex Numbers
23. Problem 1: Equality of Complex Number
24. Expression of the Polynomial P ( z ) as a Product of Linear Factors
25. Problem 1: Transitive Law of Complex Number
26. Problem-Equality of Complex Number
27. Quadratic Equation of Complex Variables
28. Problem-Transitive Law of Complex Number
29. Division Property of Complex Numbers
30. Additive Inverse and Multiplicative Inverse of Complex Numbers
31. Commutative Property of Complex Numbers
32. Problem 1: Addition of Complex Number
33. Problem-Addition of Complex Number
34. Problem 1: Properties of Complex Number
35. Problem-Properties of Complex Number
36. Additive Identity and Multiplicative Identity of Complex Numbers
37. Problem 1: Multiplication of Complex with Scalar Numbers
38. Associative Property of Complex Numbers
39. Problem-Scalar Multiplication of Complex Numbers
40. The Distributive Property of Complex Numbers
41. Problem 1: Multiplication of Complex Numbers
42. Problem-Multiplication of Complex Numbers
43. Problem 1: Subtraction of Complex Numbers
44. Problem-Subtraction of Complex Numbers
45. Problem 1: Division of Complex Numbers
46. Problem-Division of Complex Numbers
47. Problem 1: Division Property of Complex Numbers
48. Problem-Division Property of Complex Numbers
49. Problem-Commutative Property of Complex Numbers
50. Problem-Associative Property of Complex Numbers
51. Problem-The Distributive Property of Complex Numbers
52. Problem-Additive Identity and Multiplicative Identity of Complex Numb
53. Problem-Additive Inverse and Multiplicative Inverse of Complex Numbers
54. Problem-Solution of Simultaneous Linear Equations with Complex Co-eff
55. Problem-Expression of the Polynomial P ( z ) as a Product of Linear F
56. Problem-Quadratic Equation of Complex Variables
 
1.5: The Real Line
1. Presenting Rational Numbers on Number Line
2. Problem-Decimal Representation of Rational Number
3. Presenting Irrational Numbers on Number Line
4. Problem-Argand Diagram
5. Cartesian Coordinate System & Cartesian Plane
6. Problem-Decimal Representation of Irrational Number
7. Problem-Modulus of Complex Number
8. Problem 1: Cartesian Coordinate System & Cartesian Plane
 
1.6: Geometrical Representation of Complex Numbers
1. Argand Diagram
2. Modulus of Complex Number
3. Problem-Argand Diagram
4. The Order Relations
5. Theorems on Complex Number
6. More on Theorems on Complex Numbers
7. Problem-The Order Relations
8. Vector Interpretation of Complex Numbers
9. The Triangle Inequality
10. Problem-Modulus of Complex Number
11. Polar Form of a Complex Number
12. Properties of the Arguments
13. Problem-Theorems on Complex Number
14. Formula for Finding the Principal Argument
15. Problem-Vector Interpretation of Complex Numbers
16. Problem-The Triangle Inequality
17. Problem-Polar Form of a Complex Number
18. Problem2-Polar Form of a Complex Number
19. Problem-Properties of the Arguments
20. Problem-Formula for Finding the Principal Argument
 
1.7: To Find Real and Imaginary Parts of ( x + i y ) ^n
1. Real and Imaginary parts of Expression of Power n
 

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