1.Algebra Booster

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Contents
Descartes Rule of Signs 2.6
Concept of solving Algebraic In-equation 2.6
Equation Containing Absolute Values 2.6
Irrational Equations 2.7
Irrational In-equations 2.7
Exponential Equations 2.7
Exponential In-equations 2.8
Exercises 2.8
Answers 2.28
Hints and Solutions 2.31
Chapter 3 Logarithm 3.1–3.31
Introduction 3.1
Basic Formulae on Logarithm 3.1
Logarithmic Equation 3.2
Logarithmic In-equation 3.2
Conceptual Problem 3.2
Conceptual Problem 3.4
Conceptual Problem 3.6
Exercises 3.8
Answers 3.14
Hints and Solutions 3.15
Chapter 4 Complex Numbers 4.1–4.89
Introduction 4.1
Algebra of Complex Numbers 4.1
Equality of Complex Numbers 4.2
Conjugate of Complex Numbers 4.2
Modulus of a Complex Number 4.2
Argument of a Complex Number 4.3
Principal Value of Argument of a Complex Number z 4.3
Representation of a Complex Number 4.4
Square Root of a Complex Number 4.5
Cube Roots of Unity 4.5
Properties of Cube Roots of Unity 4.5
Demoivre’s Theorem 4.6
nth Roots of Unity 4.6
Rotation 4.8
Loci in a Complex Plane 4.11
Ptolemy’s Theorem 4.14
Exercises 4.14
Answers 4.31
Hints and Solutions 4.34
Chapter 5 Permutations and Combinations 5.1–5.53
Factorial Notation 5.1
Exponent of a Prime p in (n)! 5.1
Fundamental Principle of Counting 5.1
Permutations 5.1
Sum of Numbers 5.1
Permutation with Repetition 5.1
Permutations of Alike Objects 5.1
Restricted Permutations 5.2
Rank of a Word in Dictionary 5.2
Gap Method 5.2
Circular Permutations 5.2