Chapter 1 Numbers System 

1.1: Introduction

1. Introduction to Real Numbers
2. Problem-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. Presenting Irrational Numbers on Number Line
4. Problem-Decimal Representation of Irrational Number
5. Proving Square Root of Prime Number is Irrational Number
6. Problem 1: Presenting Irrational Numbers on Number Line
7. Problem-Proving Square Root of Prime Number is Irrational Number

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. Additive Identity & Additive Inverse
6. Commutative Law
7. Problem 1: Closure Law of Rational Numbers
8. Multiplicative Identity & Inverse
9. Distributive Law
10. Commutative law under Subtraction and Division
11. Problem-Commutative Law
12. Reflexive And Symmetric Property of Equality
13. Transitive Property of Equality
14. Additive Property of Equality
15. Associative law of Subtraction and Division
16. Multiplicative Property of Equality
17. Problem-Associative Law
18. Problem 1: Associative Law
19. Cancellation Property of Equality
20. Trichotomy Property of Inequality
21. Transitive Property of Inequality
22. Problem-Additive Identity & Additive Inverse
23. Problem 1: Additive Identity & Additive Inverse
24. Additive Property of Inequality
25. Multiplicative Property of Inequality
26. Inequality Multiplicative Inverse
27. Problem-Multiplicative Identity & 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. Definition of Complex Number
3. Problem-Complex Number Introduction
4. Problem 1: Complex Number Introduction
5. Conjugate of Complex Number
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. Problem 1: Conjugate of Complex Number
13. Addition of Complex Number
14. Multiplication of Complex with Scalar Numbers
15. Problem 2: Conjugate of Complex Number
16. Multiplication of Complex Numbers
17. Problem-Conjugate of Complex Number
18. Subtraction of Complex Numbers
19. Division of Complex Numbers
20. Problem 1: Equality of Complex Number
21. Problem-Equality of Complex Number
22. Division Property of Complex Numbers
23. Additive Inverse and Multiplicative Inverse of Complex Numbers
24. Problem 1: Properties of Complex Number
25. Commutative Property of Complex Numbers
26. Problem-Properties of Complex Number
27. Associative Property of Complex Numbers
28. The Distributive Property of Complex Numbers
29. Problem 1: Reflexive & Symmetric Law of Complex Number
30. Additive Identity and Multiplicative Identity of Complex Numbers
31. Problem-Reflexive & Symmetric Law of Complex Number
32. Solution of Simultaneous Linear Equations with Complex Co-efficients
33. Expression of the Polynomial P ( z ) as a Product of Linear Factors
34. Quadratic Equation of Complex Variables
35. Problem 1: Transitive Law of Complex Number
36. Problem-Transitive Law of Complex Number
37. Problem 1: Addition of Complex Number
38. Problem-Addition of Complex Number
39. Problem 1: Multiplication of Complex with Scalar Numbers
40. Problem-Scalar Multiplication 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 Number
53. Problem-Additive Inverse and Multiplicative Inverse of Complex Numbers
54. Problem-Solution of Simultaneous Linear Equations with Complex Co-efficient
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. Problem 2 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
2.Problem Real and Imaginary parts of Expression of Power n