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. 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

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. Problem 1: Closure Law of Rational Numbers
5. Commutative Law
6. Commutative law under Subtration and Division
7. Problem-Commutative Law
8. Associative Law
9. Associative law of Subtraction and Division
10. Problem-Associative Law
11. Problem 1: Associative Law
12. Additive Identity & Additive Inverse
13. Problem-Additive Identity & Additive Inverse
14. Problem 1: Additive Identity & Additive Inverse
15. Multiplicative Identity & Inverse
16. Problem-Multiplicative Identity & Inverse
17. Problem 1: Multiplicative Identity & Inverse
18. Distributive Law
19. Distributive Property of Multiplication over Subtraction
20. Problem-Distributive Law
21. Problem 1: Distributive Law
22. Problem 1: Distributive law of Multiplication over Subtraction
23. Trichotomy Property of Inequality
24. Problem-Trichotomy Property of Inequality
25. Problem 1: Trichotomy Property of Inequality
26. Reflexive And Symmetric Property of Equality
27. Problem-Reflexive And Symmetric Property of Equality
28. Transitive Property of Equality
29. Problem-Transitive Property of Equality
30. Problem 1: Transitive Property of Equality
31. Additive Property of Equality
32. Problem-Additive Property of Equality
33. Multiplicative Property of Equality
34. Problem-Multiplicative Property of Equality
35. Cancellation Property of Equality
36. Problem-Cancellation Property of Equality
37. Problem 1: Cancellation Property of Equality
38. Density Property
39. Problem-Density Property
40. Archimedian Property of Inequality
41. Problem-Transitive Property of Inequality
42. Problem 1: Transitive Property of Inequality
43. Additive Property of Inequality
44. Problem-Additive Property of Inequality
45. Multiplicative Property of Inequality
46. Problem 1: Multiplicative Property of Inequality
47. Inequality Multiplicative Inverse
48. Problem-Inequality Multiplicative Inverse
49. Indeterminate Form
50. Golden Rule of Fractions
51. Principle of Equality of Fractions
52. Rule for Quotient of Fractrions

1.4: 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. Conjugate of Complex Number
8. Problem 1: Conjugate of Complex Number
9. Problem 2: Conjugate of Complex Number
10. Problem-Conjugate of Complex Number
11. Equality of Complex Number
12. Problem 1: Equality of Complex Number
13. Problem-Equality of Complex Number
14. Properties of Complex Number
15. Problem 1: Properties of Complex Number
16. Problem-Properties of Complex Number
17. Reflexive & Symmetric Law of Complex Number
18. Problem 1: Reflexive & Symmetric Law of Complex Number
19. Problem-Reflexive & Symmetric Law of Complex Number
20. Transitive Law of Complex Number
21. Problem 1: Transitive Law of Complex Number
22. Problem-Transitive Law of Complex Number
23. Addition of Complex Number
24. Problem 1: Addition of Complex Number
25. Problem-Addition of Complex Number
26. Multiplication of Complex with Scalar Numbers
27. Problem 1: Multiplication of Complex with Scalar Numbers
28. Problem-Scalar Multiplication of Complex Numbers
29. Multiplication of Complex Numbers
30. Problem 1: Multiplication of Complex Numbers
31. Problem-Multiplication of Complex Numbers
32. Subtraction of Complex Numbers
33. Problem 1: Subtraction of Complex Numbers
34. Problem-Subtraction of Complex Numbers
35. Division of Complex Numbers
36. Problem 1: Division of Complex Numbers
37. Problem-Division of Complex Numbers
38. Division Property of Complex Numbers
39. Problem 1: Division Property of Complex Numbers
40. Problem-Division Property of Complex Numbers
41. Commutative Property of Complex Numbers
42. Problem-Commutative Property of Complex Numbers
43. Associative Property of Complex Numbers
44. Problem-Associative Property of Complex Numbers
45. The Distributive Property of Complex Numbers
46. Problem-The Distributive Property of Complex Numbers
47. Additive Identity and Multiplicative Identity of Complex Numbers
48. Problem-Additive Identity and Multiplicative Identity of Complex Numb
49. Additive Inverse and Multiplicative Inverse of Complex Numbers
50. Problem-Additive Inverse and Multiplicative Inverse of Complex Numbers
51. Solution of Simultaneous Linear Equations with Complex Co-efficients
52. Problem-Solution of Simultaneous Linear Equations with Complex Co-eff
53. Expression of the Polynomial P ( z ) as a Product of Linear Factors
54. Problem-Expression of the Polynomial P ( z ) as a Product of Linear F
55. Quadratic Equation of Complex Variables
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. Problem-Argand Diagram
4. Presenting Irrational Numbers on Number Line
5. Problem-Decimal Representation of Irrational Number
6. Problem-Modulus of Complex Number
7. Cartesian Coordinate System & Cartesian Plane
8. Problem 1: Cartesian Coordinate System & Cartesian Plane

1.6: Geometrical Representation of Complex Numbers

1. Argand Diagram
2. Problem-Argand Diagram
3. The Order Relations
4. Problem-The Order Relations
5. Modulus of Complex Number
6. Problem-Modulus of Complex Number
7. Theorems on Complex Number
8. More on Theorems on Complex Numbers
9. Problem-Theorems on Complex Number
10. Vector Interpretation of Complex Numbers
11. Problem-Vector Interpretation of Complex Numbers
12. The Triangle Inequality
13. Problem-The Triangle Inequality
14. Polar Form of a Complex Number
15. Problem-Polar Form of a Complex Number
16. Problem2-Polar Form of a Complex Number
17. Properties of the Arguments
18. Problem-Properties of the Arguments
19. Formula for Finding the Principal Argument
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