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Why Complex Numbers? (5 of 5: Where to now?)
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Complex Numbers
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- 1 Introduction to Complex Numbers (1 of 2: The Backstory)
- 2 Introduction to Complex Numbers (2 of 2: Why Algebra Requires Complex Numbers)
- 3 Who cares about complex numbers??
- 4 Why Complex Numbers? (1 of 5: Atoms & Strings)
- 5 Why Complex Numbers? (2 of 5: Impossible Roots)
- 6 Why Complex Numbers? (3 of 5: The Imaginary Unit)
- 7 Why Complex Numbers? (4 of 5: Turning the key)
- 8 Why Complex Numbers? (5 of 5: Where to now?)
- 9 Complex Arithmetic (1 of 2: Addition & Multiplication)
- 10 Complex Arithmetic (2 of 2: Conjugates & Division)
- 11 Square Roots of Complex Numbers (1 of 2: Establishing their nature)
- 12 Square Roots of Complex Numbers (2 of 2: Introductory example)
- 13 Linear Factorisation of Polynomials (1 of 2: Working in the Complex Field)
- 14 Linear Factorisation of Polynomials (2 of 2: Introductory example)
- 15 Manipulating Complex Numbers for Purely Real Results
- 16 Powers of a Complex Number (example question)
- 17 Complex Numbers as Vectors (1 of 3: Introduction & Addition)
- 18 Complex Numbers as Vectors (2 of 3: Subtraction)
- 19 Complex Numbers as Vectors (3 of 3: Using Geometric Properties)
- 20 Vectors (1 of 4: Outline of vectors and their ability to represent complex number)
- 21 Vectors (2 of 4: Representing addition & subtraction of complex numbers with vectors)
- 22 Vectors (3 of 4: Geometrically representing multiplication of complex numbers with vectors)
- 23 Vectors (4 of 4: Outlining the usefulness of vectors in representing geometry)
- 24 Complex Numbers - Mod-Arg Form (1 of 5: Introduction)
- 25 Complex Numbers - Mod-Arg Form (2 of 5: Visualising Modulus & Argument)
- 26 Complex Numbers - Mod-Arg Form (3 of 5: Calculating the Modulus)
- 27 Complex Numbers - Mod-Arg Form (4 of 5: Conversion Example 1)
- 28 Complex Numbers - Mod-Arg Form (5 of 5: Conversion Example 2)
- 29 Multiplying Complex Numbers in Mod-Arg Form (1 of 2: Reconsidering powers of i)
- 30 Multiplying Complex Numbers in Mod-Arg Form (2 of 2: Generalising the pattern)
- 31 Relationships Between Moduli & Arguments in Products of Complex Numbers
- 32 De Moivre's Theorem
- 33 How to graph the locus of |z-1|=1
- 34 Understanding Complex Quotients & Conjugates in Mod-Arg Form
- 35 Complex Numbers as Points (1 of 4: Geometric Meaning of Addition)
- 36 Complex Numbers as Points (2 of 4: Geometric Meaning of Subtraction)
- 37 Complex Numbers as Points (3 of 4: Geometric Meaning of Multiplication)
- 38 Complex Numbers as Points (4 of 4: Second Multiplication Example)
- 39 Introduction to Radians (1 of 3: Thinking about degrees)
- 40 Introduction to Radians (2 of 3: Defining a better way)
- 41 Introduction to Radians (3 of 3: Definition + Why Radians Aren't Units)
- 42 Complex Roots (1 of 5: Introduction)
- 43 Complex Roots (2 of 5: Expanding in Rectangular Form)
- 44 Complex Roots (3 of 5: Through Polar Form Using De Moivre's Theorem)
- 45 Complex Roots (4 of 5: Through Polar Form Generating Solutions)
- 46 Complex Roots (5 of 5: Flowing Example - Solving z^6=64)
- 47 Using Inverse tan to find arguments? (1 of 2: Why it doesn't work... Sometimes)
- 48 Using Inverse tan to find arguments? (2 of 2: Why it works... Sometimes)
- 49 Graphs on the Complex Plane [Continued] (1 of 4: What's behind the graph?)
- 50 Graphs on the Complex Plane [Continued] (2 of 4: Finding Regions of Inequality by Testing Points)
- 51 Graphs on the Complex Plane (3 of 4: Geometry of arg(z)-arg(z-1))
- 52 Graphs on the Complex Plane (4 of 4: Exploring how the argument traced the graph)
- 53 Further Graphs on the Complex Plane (1 of 3: Geometrical Representation of Moduli)
- 54 Further Graphs on the Complex Plane (2 of 3: Algebraically verifying Graphs concerning the Moduli)
- 55 Further Graphs on the Complex Plane (3 of 3: Geometrical Representation of Arguments)
- 56 Graphs in the Complex Plane (1 of 4: Introductory Examples)
- 57 Graphs in the Complex Plane (2 of 4: Graphing Complex Inequalities)
- 58 Graphs in the Complex Plane (3 of 4 : Shifting the Point of Reference)
- 59 Graphs in the Complex Plane (4 of 4: Where is the argument measured from?)
- 60 The Triangle Inequalities (1 of 3: Sum of Complex Numbers)
- 61 The Triangle Inequalities (2 of 3: Discussing Specific Cases)
- 62 The Triangle Inequalities (3 of 3: Difference of Complex Numbers)
- 63 DMT and Trig Identities (1 of 4: Deriving multi-angle identities with compound angles)
- 64 DMT and Trig Identities (2 of 4: Using De Moivre's Theorem and Binomial Expansions)
- 65 DMT and Trig Identities (3 of 4: Deriving tan expression from cos and sin)
- 66 DMT and Trig Identities (4 of 4: Using Multi-angle formula to solve polynomials)
- 67 Complex Conjugate Root Theorem (1 of 4: Using DMT and Polar Form to solve for Complex Roots)
- 68 Complex Conjugate Root Theorem (2 of 4: Introduction to the Conjugate Root Theorem)
- 69 Complex Conjugate Root Theorem (3 of 4: Geometrical Shape represented by Conjugate Root Theorem)
- 70 Complex Conjugate Root Theorem (4 of 4: Using Factorisation to find patterns with Roots of Unity)
- 71 Complex Numbers (1 of 6: Solving Harder Complex Numbers Questions) [Student requested problem]
- 72 Complex Numbers (2 of 6: Solving Harder Complex Numbers Questions) [Student Requested Problem]
- 73 Complex Numbers (3 of 6: Harder Complex Numbers Question) [Student Requested Problem]
- 74 Complex Numbers (4 of 6: Harder Complex Numbers Questions) [Student Requested Problem]
- 75 Complex Numbers (5 of 6: Complex Numbers Proofs [Using the Conjugate])
- 76 Complex Numbers (6 of 6: Finishing off the Proof)
- 77 2016 HSC - Complex Numbers on Unit Circle (1 of 2: Considering Re & Im Parts)
- 78 2016 HSC - Complex Numbers on Unit Circle (2 of 2: Evaluating the arguments)
- 79 2016 HSC - Complex Identity Proof (1 of 3: Convert to polar form)
- 80 2016 HSC - Complex Identity Proof (2 of 3: Using binomial theorem)
- 81 2016 HSC - Complex Identity Proof (3 of 3: Combining results)
- 82 Complex Numbers Question (Finding the greatest value of |z| if |z-4/z|=2)
- 83 Argand Diagram / Locus Question
- 84 The Most Beautiful Identity (1 of 8: Introducing Complex Numbers)
- 85 The Most Beautiful Identity (2 of 8: Same number, different clothes)
- 86 The Most Beautiful Identity (3 of 8: The Complex Plane)
- 87 The Most Beautiful Identity (4 of 8: Polar Form)
- 88 The Most Beautiful Identity (5 of 8: Polynomial Interpolation)
- 89 The Most Beautiful Identity (6 of 8: Taylor Series)
- 90 The Most Beautiful Identity (7 of 8: Revisiting Polar Form)
- 91 The Most Beautiful Identity (8 of 8: Conclusion)
- 92 Geometry of Complex Numbers (1 of 6: Radians)
- 93 Geometry of Complex Numbers (2 of 6: Real vs. Complex)
- 94 Geometry of Complex Numbers (3 of 6: Real Arithmetic)
- 95 Geometry of Complex Numbers (4 of 6: The Complex Plane)
- 96 Geometry of Complex Numbers (5 of 6: Polar Form)
- 97 Geometry of Complex Numbers (6 of 6: Conversion Between Forms)
- 98 Graphing with Complex Numbers (1 of 3: Initial algebraic expansion)
- 99 Graphing with Complex Numbers (2 of 3: Determining the region)
- 100 Graphing with Complex Numbers (3 of 3: Is |z₁z₂| equal to |z₁| × |z₂|?)
- 101 Curves and Regions on the Complex Plane (1 of 4: Introductory example plotting |z|=5 geometrically)
- 102 Curves and Regions on the Complex Plane (2 of 4: Deciphering terminology to plot complex numbers)
- 103 Curves and Regions on the Complex Plane (3 of 4: Simplifying expressions to plot on a complex plane)
- 104 Curves and Regions on the Complex Plane (4 of 4: Plotting simultaneous shifted complex numbers)
- 105 Parallelogram Law (Geometrically representing the addition of complex numbers with vectors)
- 106 Complex Conjugate Root Theorem (Formal Proof)
- 107 Complex Roots (1 of 5: Observing Complex Conjugate Root Theorem through seventh roots of unity)
- 108 Complex Roots (2 of 5: Using Trigonometrical Identities & Conjugates to solve an equation)
- 109 Complex Roots (3 of 5: Using DMT to solve an equation of roots of unity)
- 110 Complex Roots (4 of 5: Using Polynomial Identities to prove unity identities)
- 111 Complex Roots (5 of 5: Using Geometric Progression to find factors of ω^n - 1)
- 112 Square Roots of Complex Numbers
- 113 Polynomials w/ Complex Roots (interesting exam question)
- 114 Interesting Complex Polynomial Question (1 of 2: Factorisation)
- 115 Interesting Complex Polynomial Question (2 of 2: Trigonometric Result)