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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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