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M-Power Sitedocs

AoPS - Lession 5, Compplex Plane Solutions

M-Power Sitedocs

M-Power Mathmatics Sitedocs
Art of Problem Solving
Art of Problem Solving
- Critical Thinking
- Critical Thinking Framework
  Critical Thinking Framework
- Pillars of Cognition
  Pillars of Cognition
- I ❤️ Puzzles
  I ❤️ Puzzles
  - Puzzle 1 - What is my number?
  - Puzzle 2 - Magic Square, 3x3
  - Puzzle 3 - Magic Square, 4x4
  - Puzzle 4 - Frog and the Stairs
  - Logic Puzzles
    Logic Puzzles
    
    Turtle and the Hare
    
    Fruit Basket
    
    Three Weighty Coins
    
    River Crossing
    
    Jeaulous Husband
    
    Counterfeit Coins
- Math Competitions
  Math Competitions
  - AMC-8
    AMC-8
    
    Problem Set 1
    
    Problem Set 2
  - AMC 10
    AMC 10
    
    Problem Set 1
  - AMC 12
    AMC 12
    
    Problem Set 1
  - AIME
    AIME
    
    Problem Set 1
  - Olympiad
    Olympiad
    
    Problem Set 1
- Math Excursions
  Math Excursions
  - Did You Know?
  - Patterns in Numbers
    Patterns in Numbers
    
    Patterns in Nature
    
    Hidden Patterns
  - Number Shapes
- Mental Excercise
  Mental Excercise
- Tools & Resources
Language of Math
Language of Math
- Semantics
  Semantics
- Symbols and Notations
  Symbols and Notations
  - Mathematic Notation & Syntax
  - Arithmetic Operators
  - Logic Notation
  - Set Notation
  - Sigma Notation
  - Quantifiers
    Quantifiers
    
    Logic Quantifiers
    
    Set Quantifiers
    
    What's the Difference
- Algebraic Equations
  Algebraic Equations
- Objects & Labels
  Objects & Labels
  - Attributes & Properties
  - Mathematical Objects
Elementary Mathematics
Elementary Mathematics
- Definition & Properties
  Definition & Properties
  - Notion of Units
  - Number Line
  - Constructs Used in Proofs
  - Sets, Lists, Tuples
  - Properties of Numbers
    Properties of Numbers
    
    General Properties of Numbers
    
    Properties of Zero
    
    Properties of One
    
    Properties of Natural Numbers
    
    Properties of Negative Number
    
    Properties of Infinity
    
    Properties of Real
    
    Properties of Complex Numbers
    
    Properties of Composites
    
    Properties of Primes & Coprimes
    
    Properties of Parity
  - Properties of Structures
    Properties of Structures
    
    Properties of Sets
    
    Properties of Set-like Structures
- Number Sets
  Number Sets
  - Number Class
  - Natural Numbers
  - Integers
  - Real Numbers
  - Complex Numbers
    Complex Numbers
    
    Introduction
    
    A Brief History
    
    Complex Plane
    
    Complex Magnitude
    
    Polar Notation
- Number System
  Number System
  - Decimal - Base 10
  - Binary - Base 2
    Binary - Base 2
    
    Introduction
    
    Exercises
  - Hexadecimal - Base 16
- Number Patterns
  Number Patterns
  - Why Find Patterns?
  - Patterns with Integers
  - Generalization Through Patterns
    Generalization Through Patterns
    
    Generalization Process Using Patterns
    
    Sum of First n Natural Numbers
    
    Derived Formulas & Theorems through Pattern Observation
    Derived Formulas & Theorems through Pattern Observation
    
    Basic Formulas
    
    Fundamental Theorems
  - Montessori Bionmial Squares and Cubes
    Montessori Bionmial Squares and Cubes
    
    Bionomial Squares
    
    Bionomial Cubes
    
    Bionomial Cubes & Pathagorean
- Number Operations
  Number Operations
  - Aggregation
    Aggregation
    
    Aggregation in Mathematics
  - Segmentation
    Segmentation
    
    Segmentation in Mathematics
    
    Divisibility & Grouping
- Factors & Multiples
  Factors & Multiples
- GCF & LCM
  GCF & LCM
- Quotients and Remainders
- Rates, Ratios, Percents, & Proportions
  Rates, Ratios, Percents, & Proportions
- Coordinate Systems
  Coordinate Systems
  - Introduction
- Functions & Graphs
  Functions & Graphs
  - Introduction
- Sequences, Series & Summations
  Sequences, Series & Summations
- Appendix - Resources
  Appendix - Resources
  - Applied Math
    Applied Math
    
    Physics
    Physics
    
    Newton's 1st Law of Motion: Law of Inertia
    
    Newton's 2nd Law of Motion: Law of Acceleration
  - Cheatsheets
    Cheatsheets
    
    Core Ideas
    
    Arithmetic Formulas
    
    Factors Properties
    
    Multiples Properties
  - Problem Solving
Algebra 1
Algebra 1
- Class, Forms & Structures of Equations
  Class, Forms & Structures of Equations
  - Equations, Functions, Curves & Graphs
  - Curves & Graphs
  - Types of Equations
  - X-intercept
  - Y-intercept
  - Slope
  - Resources
    Resources
    
    Differences between Equations and Functions
    
    Differences between Curves and Graphs
- Algebraic Techniques
  Algebraic Techniques
- Methods of Solving for Variables
  Methods of Solving for Variables
- Linear Equations
  Linear Equations
  - Introduction
    Introduction
    
    Structures of Linear Equations
    
    What is a x-intercept?
    
    What is a y-intercept?
    
    What is a slope?
  - Semantic Structures
    Semantic Structures
    
    Introspection of Linear Forms
    
    Art of Deconstruction
    
    Forms of Linear Eq.
  - Linear Functions
  - Linear Curves & Graphs
- Quadratic Equations
  Quadratic Equations
  - Form & Structure
    Form & Structure
    
    Forms of Quadratics
    
    Properties of Quadratics
  - Understanding Vieta's Formula
  - Curves and Graphs
  - Methods of Solving Quadratics
    Methods of Solving Quadratics
    
    Factoring
    Factoring
    
    Methods of Factoring
    
    Factoring Techniques
    
    Complete the Square
    Complete the Square
    
    Perfect Square Trinomials
    
    Derivation of Completing the Square
    
    Methods of Completing the Square
  - Resources
    Resources
    
    Quadratic Cheatsheet
    
    Practice Problems
    Practice Problems
    
    Factoring of Quadratics
    
    Completing the Square
    
    Graphing Quadratics
    
    Vieta Methods
- Polynomials
  Polynomials
  - Forms & Structures
  - Deconstruction of Polynomials
  - Identification of Polynomials
  - Excercises
    Excercises
    
    Problem Set 1
- Appendix - Resources
  Appendix - Resources
  - Definitions
    Definitions
    
    Equations, Functions, Curves & Graphs
    
    Equations, Functions, Curves & Graphs
  - Laws & Properties
    Laws & Properties
    
    Fundamental Theorem of Arithmetic
    
    Fundamental Theorem of Algebra
    
    Laws of Equalities & Inequalities
    
    Laws of Exponents
    
    Peano Axioms
  - Theorems
    Theorems
    
    General
    
    Quadratic Thorems
    
    Pythagorean Theorem
  - Problem Solving
    Problem Solving
    
    Solve for x
    Solve for x
    
    Problem 1 - Radical
    
    Problem 2 - Simultaneous Eq.
    
    Problem 3 - Rational Powers
    
    Problem 4 - Powers
    
    Problem 5 - Linear Eq.
    
    AoPS-A1
    AoPS-A1
    
    Lesson 1
    
    Lesson 2
  - Cheatsheets
    Cheatsheets
    
    Algebraic Identities
    
    Alegrba 1 Properties & Formulas
Algebra 2
Algebra 2
- Coordinate Planes
  Coordinate Planes
- Cubic Equations
  Cubic Equations
  - Forms & Structures
- Appendix - Resources
  Appendix - Resources
  - Cartesian Plane vs Euclidean Plane
  - Cheatsheets
    Cheatsheets
    
    Algebraic Identities
    
    Alegrba 2 Properties & Formulas
    
    Trignometry Identities
  - Problem Solving
    Problem Solving
    
    AoPS-A2
    AoPS-A2
    
    Lesson 4 - Functions
    
    Lesson 5 - Complex Numbers
    
    Lesson 6 - Complex Planes
    
    Lesson 7 - Quadratics
Geometry
Geometry
- Circle
  Circle
  - Form & Structures
  - Circle Math
- Shapes
  Shapes
  - Triangles
- Appendix - Resources
  Appendix - Resources
  - Cheatsheets
    Cheatsheets
    
    Geometry Properties & Formulas
    
    Geometry Theorems
Logic
Logic
- Foundation
Modular Arithmetic
Modular Arithmetic
- Definition & Properties
  Definition & Properties
- Clock Math
- Appendix - Resources
  Appendix - Resources
  - Cheatsheets
    Cheatsheets
    
    General
  - Exercises
    Exercises
    
    Problems Set 1
Number Theory
Number Theory
- Definition & Properties
  Definition & Properties
  - Segmentation
- Factors & Multiples
- Primality
  Primality
- Divisibility
  Divisibility
- Theorems
  Theorems
- Appendix - Resources
  Appendix - Resources
  - Cheat-Sheets
    Cheat-Sheets
    
    Number Theory Theorems
    
    Count Number of Factors
    
    Exponentiation Method

AoPS - Lession 5, Compplex Plane Solutions¶

Problem 1¶

Problem Statement:

TBD