# Chapter 2: Real and Complex Numbers

2.1: Real Numbers |
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1. Introduction to Real Numbers |

2. Introduction to Rational Numbers |

3. Problem 1: Introduction to Rational Numbers |

4. Introduction to Irrational Numbers |

5. Problem 1: Introduction to Irrational Numbers |

6. Presenting Rational Numbers on Number Line |

7. Presenting Irrational Numbers on Number Line |

8. Problem 1: Presenting Irrational Numbers on Number Line |

9. Decimal Representation of Rational Number |

10. Problem 1: Decimal Representation of Rational Number |

11. Decimal Representation of Irrational Number |

2.2: Properties of Real Numbers |
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1. Closure Law of Rational Numbers |

2. Problem 1: Closure Law of Rational Numbers |

3. Commutative Law |

4. Associative Law |

5. Problem 1: Associative Law |

6. Additive Identity & Additive Inverse |

7. Problem 1: Additive Identity & Additive Inverse |

8. Multiplicative Identity & Inverse |

9. Problem 1: Multiplicative Identity & Inverse |

10. Distributive Law |

11. Problem 1: Distributive Law |

12. Reflexive And Symmetric Property of Equality |

13. Transitive Property of Equality |

14. Problem 1: Transitive Property of Equality |

15. Additive Property of Equality |

16. Multiplicative Property of Equality |

17. Cancellation Property of Equality |

18. Problem 1: Cancellation Property of Equality |

19. Trichotomy Property of Inequality |

20. Problem 1: Trichotomy Property of Inequality |

21. Transitive Property of Inequality |

22. Problem 1: Transitive Property of Inequality |

23. Additive Property of Inequality |

24. Multiplicative Property of Inequality |

25. Problem 1: Multiplicative Property of Inequality |

26. Inequality Multiplicative Inverse |

2.3: Radicals and Radicands |
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1. Square Root |

2. Problem 1: Square Root |

3. Properties of Square Root |

4. Problem 1: Properties of Square Root |

5. More on Properties of Square Root |

6. qth Root of x |

7. Problem 1: qth Root of x |

8. Properties of qth Root of x |

9. Problem 1: Properties of qth Root of x |

10. Rational Exponents |

11. Problem 1: Rational Exponents |

12. Properties of Rational Exponents |

13. Problem 1: Properties of Rational Exponents |

14. Proof of x Raise to Power Zero Equals One |

15. Problem 1: Proof of x Raise to Power Zero Equals One |

16. Transformation of Radical & Exponential Form |

17. Problem 1: Transformation of Radical & Exponential Form |

2.4: Laws of Exponents/Indices |
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1. Exponent or Index Definition |

2. Problem 1: Exponent or Index Definition |

3. Law of Sum of Power of Exponents |

4. Problem 1: Law of Sum of Power of Exponents |

5. Law of Power of Product of Exponent |

6. Problem 1: Law of Power of Product of Exponent |

7. Law of Power of Power of Exponent |

8. Problem 1: Law of Power of Power of Exponent |

9. Law of Quotient of Power with Same Base |

10. Problem 1: Law of Quotient of Power with Same Base |

11. Law of Power of a Fraction |

12. Problem 1: Law of Power of a Fraction |

13. Applications of Laws of Exponents |

14. Problem 1: Applications of Laws of Exponents |

2.5: Complex Numbers |
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1. Complex Number Introduction |

2. Problem 1: Complex Number Introduction |

3. Definition of Complex Number |

4. Problem 1: Definition of Complex Number |

5. Conjugate of Complex Number |

6. Problem 1: Conjugate of Complex Number |

7. Equality of Complex Number |

8. Problem 1: Equality of Complex Number |

9. Properties of Complex Number |

10. Problem 1: Properties of Complex Number |

11. Reflexive & Symmetric Law of Complex Number |

12. Problem 1: Reflexive & Symmetric Law of Complex Number |

13. Transitive Law of Complex Number |

14. Problem 1: Transitive Law of Complex Number |

2.6: Basic Operations on Complex Numbers |
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1. Addition of Complex Number |

2. Problem 1: Addition of Complex Number |

3. Multiplication of Complex with Scalar Numbers |

4. Problem 1: Multiplication of Complex with Scalar Numbers |

5. Multiplication of Complex Numbers |

6. Problem 1: Multiplication of Complex Numbers |

7. Subtraction of Complex Numbers |

8. Problem 1: Subtraction of Complex Numbers |

9. Division of Complex Numbers |

10. Problem 1: Division of Complex Numbers |

11. Division Property of Complex Numbers |

12. Problem 1: Division Property of Complex Numbers |

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