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Complex Numbers

Complex Numbers

Eddie Woo via YouTube Direct link

The Most Beautiful Identity (1 of 8: Introducing Complex Numbers)

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The Most Beautiful Identity (1 of 8: Introducing Complex Numbers)

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Complex Numbers

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

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