# Chapter 2: Real and Complex Numbers

2.1: Real Numbers
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
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
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
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
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
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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