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Someone asked me a question about Euler's Identity (e^iπ = --1)...
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Introduction to Complex Numbers
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- 1 Someone asked me a question about Euler's Identity (e^iπ = --1)...
- 2 Polynomials w/ Complex Roots (interesting exam question)
- 3 Exam Problem: Cubic Polynomial w/ 1 Real Root
- 4 Introduction to Complex Numbers (1 of 2: The Backstory)
- 5 Complex Arithmetic (1 of 2: Addition & Multiplication)
- 6 Complex Arithmetic (2 of 2: Conjugates & Division)
- 7 Introduction to Complex Numbers (2 of 2: Why Algebra Requires Complex Numbers)
- 8 Who cares about complex numbers??
- 9 Linear Factorisation of Polynomials (1 of 2: Working in the Complex Field)
- 10 Square Roots of Complex Numbers (1 of 2: Establishing their nature)
- 11 Square Roots of Complex Numbers (2 of 2: Introductory example)
- 12 Linear Factorisation of Polynomials (2 of 2: Introductory example)
- 13 Complex Numbers - Mod-Arg Form (1 of 5: Introduction)
- 14 Complex Numbers - Mod-Arg Form (2 of 5: Visualising Modulus & Argument)
- 15 Complex Numbers - Mod-Arg Form (3 of 5: Calculating the Modulus)
- 16 Complex Numbers - Mod-Arg Form (4 of 5: Conversion Example 1)
- 17 Complex Numbers - Mod-Arg Form (5 of 5: Conversion Example 2)
- 18 Multiplying Complex Numbers in Mod-Arg Form (1 of 2: Reconsidering powers of i)
- 19 Multiplying Complex Numbers in Mod-Arg Form (2 of 2: Generalising the pattern)
- 20 Relationships Between Moduli & Arguments in Products of Complex Numbers
- 21 Powers of a Complex Number (example question)
- 22 Understanding Complex Quotients & Conjugates in Mod-Arg Form
- 23 Manipulating Complex Numbers for Purely Real Results
- 24 Complex Numbers Question (Finding the greatest value of |z| if |z-4/z|=2)
- 25 Complex Conjugate Root Theorem (Formal Proof)
- 26 Complex Conjugate Root Theorem (1 of 2: Using the Conjugate Root Theorem to solve Polynomials)
- 27 Complex Conjugate Root Theorem (2 of 2: Alternatively solving with Long Division)
- 28 Extension II Assessment Review (1 of 5: Multiple Choice Questions Section)
- 29 Extension II Assessment Review (2 of 5: Complex Conjugate Root Theorem, DMT & Geometry)
- 30 The Most Beautiful Identity (1 of 8: Introducing Complex Numbers)
- 31 The Most Beautiful Identity (2 of 8: Same number, different clothes)
- 32 The Most Beautiful Identity (3 of 8: The Complex Plane)
- 33 The Most Beautiful Identity (4 of 8: Polar Form)
- 34 The Most Beautiful Identity (5 of 8: Polynomial Interpolation)
- 35 The Most Beautiful Identity (6 of 8: Taylor Series)
- 36 The Most Beautiful Identity (7 of 8: Revisiting Polar Form)
- 37 The Most Beautiful Identity (8 of 8: Conclusion)
- 38 Square Roots of Complex Numbers
- 39 Why √a√b isn't always equal to √ab
- 40 Geometry of Complex Numbers (1 of 6: Radians)
- 41 Geometry of Complex Numbers (2 of 6: Real vs. Complex)
- 42 Geometry of Complex Numbers (3 of 6: Real Arithmetic)
- 43 Geometry of Complex Numbers (4 of 6: The Complex Plane)
- 44 Geometry of Complex Numbers (5 of 6: Polar Form)
- 45 Geometry of Complex Numbers (6 of 6: Conversion Between Forms)
- 46 Polar Form (1 of 2: Using Complex Number examples to justify polar form's use)
- 47 Polar Form (2 of 2: Generalising to prove the multiplication identity of polar form)
- 48 Parallelogram Law (Geometrically representing the addition of complex numbers with vectors)
- 49 Solutions of (1+i)z² - z - i = 0
- 50 Graphing with Complex Numbers (1 of 3: Initial algebraic expansion)
- 51 Graphing with Complex Numbers (2 of 3: Determining the region)
- 52 Graphing with Complex Numbers (3 of 3: Is |z₁z₂| equal to |z₁| × |z₂|?)
- 53 Introducing Complex Numbers (1 of 3: History of numbers)
- 54 Introducing Complex Numbers (2 of 3: Revealing the invisible)
- 55 Introducing Complex Numbers (3 of 3: Defining fundamentals)
- 56 Complex Arithmetic (1 of 3: Basic operations)
- 57 Complex Arithmetic (2 of 3: Trigonometric identity)
- 58 Complex Arithmetic (3 of 3: Identity from ℝ component)
- 59 Further Complex Arithmetic (1 of 2: Basic questions and notation)
- 60 Further Complex Arithmetic (2 of 2: Equating components)
- 61 Introducing the Complex Plane
- 62 Exploring the Complex Plane (1 of 2: Visualising addition & subtraction)
- 63 Exploring the Complex Plane (2 of 2: Visualising multiplication)
- 64 Basics of Complex Geometry (example questions)
- 65 Introducing Polar Form (1 of 3: An alternative coordinate system)
- 66 Introducing Polar Form (2 of 3: Relationship to rectangular form)
- 67 Introducing Polar Form (3 of 3: Example conversion)
- 68 Working in Polar Form (1 of 2: Conjugate & negative)
- 69 Working in Polar Form (2 of 2: Square & reciprocal)
- 70 Distance between complex numbers
- 71 Exact value of cos(π÷12)
- 72 Quotient of Complex Numbers (1 of 2: Evaluating modulus)
- 73 Quotient of Complex Numbers (2 of 2: Evaluating argument)
- 74 Working with Moduli and Arguments (Proof Question)
- 75 Argument of the Complex Conjugate
- 76 Square Roots of a Complex Number (3 of 3: Solving in rectangular and exponential form)
- 77 Square Roots of a Complex Number (2 of 3: Principal square root)
- 78 Square Roots of a Complex Number (1 of 3: Review questions)
- 79 Proving Euler's Formula (4 of 4: Evaluating constants)
- 80 Proving Euler's Formula (3 of 4: Equating terms)
- 81 Proving Euler's Formula (2 of 4: Differentiating both sides)
- 82 Proving Euler's Formula (1 of 4: Fields)
- 83 What does an imaginary power mean?
- 84 Informal Proof of Euler's Formula (2 of 2: Trigonometric calculus)
- 85 Informal Proof of Euler's Formula (1 of 2: Exponential calculus)
