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Invidious > Channel > Eddie Woo

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YT 6 minutes 8 seconds Eddie Woo Using De Moivre's Theorem to Prove Trigonometric Identity YT 11 minutes 21 seconds Eddie Woo Understanding & Applying the Conjugate Root Theorem YT 3 minutes 56 seconds Eddie Woo Argand Diagram / Locus Question

YT 14 minutes 33 seconds Eddie Woo Interesting Complex Polynomial Question (1 of 2: Factorisation) YT 10 minutes 12 seconds Eddie Woo Interesting Complex Polynomial Question (2 of 2: Trigonometric Result) YT 10 minutes 21 seconds Eddie Woo Complex Numbers as Points (1 of 4: Geometric Meaning of Addition)

YT 7 minutes 42 seconds Eddie Woo Complex Numbers as Points (2 of 4: Geometric Meaning of Subtraction) YT 6 minutes 50 seconds Eddie Woo Complex Numbers as Points (3 of 4: Geometric Meaning of Multiplication) YT 5 minutes 34 seconds Eddie Woo Complex Numbers as Points (4 of 4: Second Multiplication Example)

YT 7 minutes 27 seconds Eddie Woo De Moivre's Theorem YT 7 minutes 59 seconds Eddie Woo How to graph the locus of |z-1|=1 YT 9 minutes 29 seconds Eddie Woo Complex Numbers as Vectors (1 of 3: Introduction & Addition)

YT 7 minutes 21 seconds Eddie Woo Complex Numbers as Vectors (2 of 3: Subtraction) YT 8 minutes 49 seconds Eddie Woo Complex Numbers as Vectors (3 of 3: Using Geometric Properties) YT 9 minutes 44 seconds Eddie Woo Complex Roots (2 of 5: Expanding in Rectangular Form)

YT 10 minutes 46 seconds Eddie Woo The Triangle Inequalities (1 of 3: Sum of Complex Numbers) YT 10 minutes 3 seconds Eddie Woo Graphs in the Complex Plane (1 of 4: Introductory Examples) YT 9 minutes 17 seconds Eddie Woo The Triangle Inequalities (2 of 3: Discussing Specific Cases)

YT 5 minutes 16 seconds Eddie Woo The Triangle Inequalities (3 of 3: Difference of Complex Numbers) YT 4 minutes 25 seconds Eddie Woo Graphs in the Complex Plane (2 of 4: Graphing Complex Inequalities) YT 11 minutes 57 seconds Eddie Woo Graphs in the Complex Plane (3 of 4 : Shifting the Point of Reference)

YT 6 minutes 42 seconds Eddie Woo Graphs in the Complex Plane (4 of 4: Where is the argument measured from?) YT 8 minutes 20 seconds Eddie Woo Further Graphs on the Complex Plane (1 of 3: Geometrical Representation of Moduli) YT 8 minutes 23 seconds Eddie Woo Further Graphs on the Complex Plane (2 of 3: Algebraically verifying Graphs concerning the Moduli)

YT 13 minutes 18 seconds Eddie Woo Further Graphs on the Complex Plane (3 of 3: Geometrical Representation of Arguments) YT 10 minutes 30 seconds Eddie Woo Graphs on the Complex Plane (3 of 4: Geometry of arg(z)-arg(z-1)) YT 7 minutes 4 seconds Eddie Woo Graphs on the Complex Plane (4 of 4: Exploring how the argument traced the graph)

YT 11 minutes 56 seconds Eddie Woo Graphs on the Complex Plane [Continued] (1 of 4: What's behind the graph?) YT 5 minutes 38 seconds Eddie Woo Graphs on the Complex Plane [Continued] (2 of 4: Finding Regions of Inequality by Testing Points) YT 11 minutes 51 seconds Eddie Woo Using Inverse tan to find arguments? (1 of 2: Why it doesn't work... Sometimes)

YT 5 minutes 55 seconds Eddie Woo Complex Roots (1 of 5: Introduction) YT 9 minutes 51 seconds Eddie Woo Complex Roots (3 of 5: Through Polar Form Using De Moivre's Theorem) YT 5 minutes 23 seconds Eddie Woo Using Inverse tan to find arguments? (2 of 2: Why it works... Sometimes)

YT 3 minutes 52 seconds Eddie Woo Complex Roots (4 of 5: Through Polar Form Generating Solutions) YT 10 minutes 28 seconds Eddie Woo Complex Roots (5 of 5: Flowing Example - Solving z^6=64) YT 10 minutes 20 seconds Eddie Woo Complex Conjugate Root Theorem (1 of 4: Using DMT and Polar Form to solve for Complex Roots)

YT 12 minutes 22 seconds Eddie Woo Complex Conjugate Root Theorem (2 of 4: Introduction to the Conjugate Root Theorem) YT 10 minutes 29 seconds Eddie Woo Complex Conjugate Root Theorem (3 of 4: Geometrical Shape represented by Conjugate Root Theorem) YT 6 minutes 28 seconds Eddie Woo Complex Conjugate Root Theorem (4 of 4: Using Factorisation to find patterns with Roots of Unity)

YT 8 minutes 31 seconds Eddie Woo DMT and Trig Identities (1 of 4: Deriving multi-angle identities with compound angles) YT 10 minutes 54 seconds Eddie Woo DMT and Trig Identities (2 of 4: Using De Moivre's Theorem and Binomial Expansions) YT 7 minutes 52 seconds Eddie Woo DMT and Trig Identities (3 of 4: Deriving tan expression from cos and sin)

YT 12 minutes 45 seconds Eddie Woo DMT and Trig Identities (4 of 4: Using Multi-angle formula to solve polynomials) YT 10 minutes 36 seconds Eddie Woo Complex Numbers (1 of 6: Solving Harder Complex Numbers Questions) [Student requested problem] YT 6 minutes 24 seconds Eddie Woo Complex Numbers (2 of 6: Solving Harder Complex Numbers Questions) [Student Requested Problem]

YT 7 minutes 54 seconds Eddie Woo Complex Numbers (3 of 6: Harder Complex Numbers Question) [Student Requested Problem] YT 7 minutes 11 seconds Eddie Woo Complex Numbers (4 of 6: Harder Complex Numbers Questions) [Student Requested Problem] YT 11 minutes 14 seconds Eddie Woo Complex Numbers (5 of 6: Complex Numbers Proofs [Using the Conjugate])

YT 6 minutes 40 seconds Eddie Woo Complex Numbers (6 of 6: Finishing off the Proof) YT 6 minutes 13 seconds Eddie Woo Roots and Coefficients (1 of 3: Using DMT & Binomial Theorem to find identities) YT 6 minutes 12 seconds Eddie Woo Roots and Coefficients (2 of 3: Using Trigonometry to solve polynomial problems)

YT 8 minutes 59 seconds Eddie Woo Roots and Coefficients (3 of 3: Using the results to find a relation in cosine) YT 5 minutes 17 seconds Eddie Woo Extension II Assessment Review (5 of 5: De Moivre's Theorem and Polynomials) YT 7 minutes 16 seconds Eddie Woo Why Complex Numbers? (1 of 5: Atoms & Strings)

YT 8 minutes 3 seconds Eddie Woo Why Complex Numbers? (2 of 5: Impossible Roots) YT 9 minutes 57 seconds Eddie Woo Why Complex Numbers? (3 of 5: The Imaginary Unit) YT 6 minutes Eddie Woo Why Complex Numbers? (4 of 5: Turning the key)

YT 9 minutes 31 seconds Eddie Woo Why Complex Numbers? (5 of 5: Where to now?) YT 7 minutes 35 seconds Eddie Woo Complex Arithmetic (1 of 2: Addition, Subtraction & Multiplication) YT 7 minutes 50 seconds Eddie Woo Complex Arithmetic (2 of 2: Division)

YT 11 minutes 42 seconds Eddie Woo Factorisation with Complex Numbers YT 5 minutes Eddie Woo Vectors (1 of 4: Outline of vectors and their ability to represent complex number) YT 7 minutes 37 seconds Eddie Woo Vectors (2 of 4: Representing addition & subtraction of complex numbers with vectors)

YT 5 minutes 33 seconds Eddie Woo Vectors (3 of 4: Geometrically representing multiplication of complex numbers with vectors) YT 10 minutes 37 seconds Eddie Woo Vectors (4 of 4: Outlining the usefulness of vectors in representing geometry) YT 12 minutes 49 seconds Eddie Woo Curves and Regions on the Complex Plane (1 of 4: Introductory example plotting |z|=5 geometrically)

YT 6 minutes 26 seconds Eddie Woo Curves and Regions on the Complex Plane (2 of 4: Deciphering terminology to plot complex numbers) YT 6 minutes 43 seconds Eddie Woo Curves and Regions on the Complex Plane (3 of 4: Simplifying expressions to plot on a complex plane) YT 7 minutes 34 seconds Eddie Woo Curves and Regions on the Complex Plane (4 of 4: Plotting simultaneous shifted complex numbers)

YT 3 minutes 52 seconds Eddie Woo Further Curves and Regions (1 of 5: Why does Sine & the Sine Rule produce an ambiguous case?) YT 11 minutes 52 seconds Eddie Woo Further Curves and Regions (2 of 5: Finding the Range of |z| ) YT 5 minutes 56 seconds Eddie Woo Further Curves and Regions (3 of 5: Finding the range of arg z)

YT 10 minutes 31 seconds Eddie Woo Further Curves and Regions (4 of 5: Geometrical expression of expressions of arg) YT 6 minutes 58 seconds Eddie Woo Further Curves and Regions (5 of 5: Using Circle properties to graph an expression of args) YT 7 minutes Eddie Woo DMT & Complex Roots (1 of 4: Reviewing geometrical expression of arg equations)

YT 11 minutes 30 seconds Eddie Woo DMT & Complex Roots (2 of 4: Using DMT to find roots of a complex polynomial) YT 7 minutes 36 seconds Eddie Woo DMT & Complex Roots (3 of 4: Using the fundamental theorem of algebra to justify number of roots) YT 6 minutes 48 seconds Eddie Woo DMT & Complex Roots (4 of 4: Solving for roots of a complex number taking advantage of DMT)

YT 11 minutes 20 seconds Eddie Woo Complex Roots (1 of 5: Observing Complex Conjugate Root Theorem through seventh roots of unity) YT 7 minutes 26 seconds Eddie Woo Complex Roots (2 of 5: Using Trigonometrical Identities & Conjugates to solve an equation) YT 4 minutes 20 seconds Eddie Woo Complex Roots (3 of 5: Using DMT to solve an equation of roots of unity)

YT 7 minutes 44 seconds Eddie Woo Complex Roots (4 of 5: Using Polynomial Identities to prove unity identities) YT 6 minutes 2 seconds Eddie Woo Complex Roots (5 of 5: Using Geometric Progression to find factors of ω^n - 1) YT 4 minutes 35 seconds Eddie Woo DMT and Trig Identities (1 of 4: Noticing a pattern in natural numbers)

YT 8 minutes 2 seconds Eddie Woo DMT and Trig Identities (2 of 4: Using Trig expansion to find the sine triple angle formula) YT 7 minutes 42 seconds Eddie Woo DMT and Trig Identities (3 of 4: Using DMT and Polynomials to verify triple angle formula for sine) YT 11 minutes 44 seconds Eddie Woo DMT and Trig Identities (4 of 4: Using Trig Identities to solve polynomial equations)

YT 8 minutes 6 seconds Eddie Woo HSC Question on Complex Numbers, Vectors & Triangle Area (1 of 2: Thinking geometrically) YT 7 minutes 21 seconds Eddie Woo HSC Question on Complex Numbers, Vectors & Triangle Area (2 of 2: Manipulating trigonometric terms) YT 8 minutes 6 seconds Eddie Woo HSC Question on Complex Numbers, Vectors & Polynomials (1 of 2: How to "explain")

YT 9 minutes 55 seconds Eddie Woo HSC Question on Complex Numbers, Vectors & Polynomials (2 of 2: Combining results) YT 9 minutes 2 seconds Eddie Woo 2016 HSC - Complex Numbers on Unit Circle (1 of 2: Considering Re & Im Parts) YT 8 minutes 3 seconds Eddie Woo 2016 HSC - Complex Numbers on Unit Circle (2 of 2: Evaluating the arguments)

YT 5 minutes 53 seconds Eddie Woo 2016 HSC - Complex Identity Proof (1 of 3: Convert to polar form) YT 5 minutes 37 seconds Eddie Woo 2016 HSC - Complex Identity Proof (2 of 3: Using binomial theorem) YT 7 minutes 24 seconds Eddie Woo 2016 HSC - Complex Identity Proof (3 of 3: Combining results)

YT 7 minutes 55 seconds Eddie Woo Semi Circles on Argand Diagrams (3 of 3: Oblique example) YT 14 minutes 52 seconds Eddie Woo Semi Circles on Argand Diagrams (2 of 3: Graphing the locus) YT 9 minutes 3 seconds Eddie Woo Semi Circles on Argand Diagrams (1 of 3: Relating the angles)

YT 10 minutes 25 seconds Eddie Woo Algebraic Proof for Opposing Rays (3 of 3: Testing cases) YT 8 minutes 42 seconds Eddie Woo Algebraic Proof for Opposing Rays (2 of 3: Generating the equation) YT 9 minutes 59 seconds Eddie Woo Algebraic Proof for Opposing Rays (1 of 3: Foundational knowledge)

YT 14 minutes 55 seconds Eddie Woo cos⁴θ Identity YT 13 minutes 57 seconds Eddie Woo Graphs in the Complex Plane (3 of 3: Opposing rays) YT 11 minutes 59 seconds Eddie Woo Graphs in the Complex Plane (2 of 3: Algebraic method)

YT 8 minutes 16 seconds Eddie Woo Graphs in the Complex Plane (1 of 3: Perpendicular bisector - visual method) YT 18 minutes 7 seconds Eddie Woo Complex Polynomial Identity Question (4 of 4: Roots & coefficients) YT 12 minutes 37 seconds Eddie Woo Complex Polynomial Identity Question (3 of 4: de Moivre's Theorem)

YT 6 minutes 25 seconds Eddie Woo Complex Polynomial Identity Question (2 of 4: Difference of cubes) YT 13 minutes 45 seconds Eddie Woo Complex Polynomial Identity Question (1 of 4: Quadratic factors) YT 12 minutes 49 seconds Eddie Woo Sum & Product of Cosines (3 of 3: Drawing ℝ conclusions)

YT 11 minutes 8 seconds Eddie Woo Sum & Product of Cosines (2 of 3: Simplifying with conjugates) YT 11 minutes 26 seconds Eddie Woo Sum & Product of Cosines (1 of 3: 9th roots of unity) YT 14 minutes 17 seconds Eddie Woo Nth Roots of a ℂ Number (2 of 2: Example problem)

YT 9 minutes 53 seconds Eddie Woo Nth Roots of a ℂ Number (1 of 2: General form) YT 9 minutes 39 seconds Eddie Woo Roots of Unity (2 of 2: Insights from polar & exponential forms) YT 13 minutes 11 seconds Eddie Woo Roots of Unity (1 of 2: Evaluating the cube roots)

YT 11 minutes 5 seconds Eddie Woo Complex Conjugate Root Theorem (2 of 2: Other conjugate properties) YT 11 minutes 13 seconds Eddie Woo Complex Conjugate Root Theorem (1 of 2: Conjugate of a sum) YT 9 minutes 56 seconds Eddie Woo Solving Higher Degree Trigonometric Equations (3 of 3: Finding solutions)

YT 8 minutes 14 seconds Eddie Woo Solving Higher Degree Trigonometric Equations (2 of 3: Combining results into proof) YT 10 minutes 28 seconds Eddie Woo Solving Higher Degree Trigonometric Equations (1 of 3: Initial use of de Moivre's Theorem) YT 11 minutes 29 seconds Eddie Woo Equations with Complex Solutions (2 of 2: Solving & factorising)

YT 7 minutes 32 seconds Eddie Woo Equations with Complex Solutions (1 of 2: Relation to square roots) YT 18 minutes 44 seconds Eddie Woo Polynomials with Trigonometric Solutions (3 of 3: Simplifying with identities) YT 16 minutes 10 seconds Eddie Woo Polynomials with Trigonometric Solutions (2 of 3: Substitute & solve)

YT 18 minutes 52 seconds Eddie Woo Polynomials with Trigonometric Solutions (1 of 3: de Moivre's Theorem) YT 7 minutes 50 seconds Eddie Woo Trigonometric Expansions from Complex Numbers (3 of 3: General compound angles) YT 9 minutes 39 seconds Eddie Woo Trigonometric Expansions from Complex Numbers (2 of 3: Double angle results)

YT 11 minutes 15 seconds Eddie Woo Trigonometric Expansions from Complex Numbers (1 of 3: Concept map) YT 8 minutes 1 second Eddie Woo Using de Moivre's Theorem - example question (2 of 2: Purely imaginary) YT 8 minutes 56 seconds Eddie Woo Using de Moivre's Theorem - example question (1 of 2: Purely real)

YT 12 minutes 12 seconds Eddie Woo Proving de Moivre's Theorem (2 of 2: Derivation & example problem) YT 11 minutes 18 seconds Eddie Woo Proving de Moivre's Theorem (1 of 2: Prologue) YT 8 minutes 19 seconds Eddie Woo Arcs on the Complex Plane (1 of 4: Review questions)

YT 8 minutes 23 seconds Eddie Woo Arcs on the Complex Plane (3 of 4: Identifying length and direction) YT 11 minutes 10 seconds Eddie Woo Arcs on the Complex Plane (2 of 4: Exploring circle properties) YT 7 minutes 4 seconds Eddie Woo Arcs on the Complex Plane (4 of 4: Cartesian equation)

YT 9 minutes 27 seconds Eddie Woo Angles in the Same Segment YT 6 minutes 43 seconds Eddie Woo Algebraic Approach for Major Arc (1 of 2: Foundational steps) YT 11 minutes 51 seconds Eddie Woo Algebraic Approach for Major Arc (2 of 2: Identifying intercept & equation)

YT 9 minutes 23 seconds Eddie Woo Max/Min Value of |z| (1 of 2: Geometric solution) YT 14 minutes 41 seconds Eddie Woo Max/Min Value of |z| (2 of 2: Triangle inequality) YT 12 minutes 11 seconds Eddie Woo Investigating de Moivre's Theorem (1 of 3: Why must we be cautious?)

YT 8 minutes 58 seconds Eddie Woo Investigating de Moivre's Theorem (2 of 3: Infinite values for i-th powers?!) YT 16 minutes Eddie Woo Investigating de Moivre's Theorem (3 of 3: Proof by mathematical induction) YT 10 minutes 26 seconds Eddie Woo Varying |z| & Argz on a Locus

YT 16 minutes 49 seconds Eddie Woo Maximising Sum of Moduli (1 of 3: Geometric approach) YT 10 minutes 32 seconds Eddie Woo Maximising Sum of Moduli (2 of 3: Differentiation) YT 8 minutes 11 seconds Eddie Woo Maximising Sum of Moduli (3 of 3: Interpreting stationary points)

YT 9 minutes 57 seconds Eddie Woo Sketching (z-1)÷(z-i) (1 of 2: When it's real) YT 11 minutes 15 seconds Eddie Woo Sketching (z-1)÷(z-i) (2 of 2: When it's imaginary) YT 10 minutes 11 seconds Eddie Woo Complex Numbers Exam Review (1 of 4: Visualising & Manipulating Arithmetic)

YT 9 minutes 51 seconds Eddie Woo Complex Numbers Exam Review (2 of 4: Proving i^i is real, identity proof) YT 13 minutes 33 seconds Eddie Woo Complex Numbers Exam Review (3 of 4: Cube roots of unity) YT 10 minutes 24 seconds Eddie Woo Complex Numbers Exam Review (4 of 4: Locus; polynomial identity)

YT 15 minutes 28 seconds Eddie Woo Prove arg(z₁z₂) = arg(z₁+z₂)² (1 of 2: Preliminary thoughts) YT 16 minutes 51 seconds Eddie Woo Prove arg(z₁z₂) = arg(z₁+z₂)² (2 of 2: Geometric approach) YT 7 minutes Eddie Woo Complex Geometry - Square Problem (1 of 2: Complex numbers → vectors)

YT 9 minutes Eddie Woo Complex Geometry - Square Problem (2 of 2: Vectors → complex numbers) YT 13 minutes 24 seconds Eddie Woo Complex Geometry - Equilateral Triangle (3 of 3: Vector proof) YT 10 minutes 32 seconds Eddie Woo Complex Geometry - Equilateral Triangle (2 of 3: Algebraic method)

YT 14 minutes 36 seconds Eddie Woo Complex Geometry - Equilateral Triangle (1 of 3: Arithmetic proof) YT 14 minutes 25 seconds Eddie Woo The Basel Problem (9 of 9: Squeeze law) YT 15 minutes 58 seconds Eddie Woo The Basel Problem (8 of 9: Returning to trigonometric terms)

YT 10 minutes 24 seconds Eddie Woo The Basel Problem (7 of 9: Manipulating the polynomial integral) YT 14 minutes 32 seconds Eddie Woo The Basel Problem (5 of 9: Telescoping sum) YT 7 minutes 44 seconds Eddie Woo The Basel Problem (6 of 9: Equations → inequalities)

YT 18 minutes 14 seconds Eddie Woo The Basel Problem (4 of 9: Introducing x² to the integrand) YT 7 minutes 57 seconds Eddie Woo The Basel Problem (3 of 9: Integration by *different* parts) YT 8 minutes 41 seconds Eddie Woo The Basel Problem (1 of 9: Prologue)

YT 15 minutes 29 seconds Eddie Woo The Basel Problem (2 of 9: Recurrence relation) YT 11 minutes 23 seconds Eddie Woo Centre of a Major Arc (5 of 5: Algebraic proof) YT 12 minutes 26 seconds Eddie Woo Centre of a Major Arc (4 of 5: Inscribed equilateral triangle)

YT 12 minutes 15 seconds Eddie Woo Centre of a Major Arc (3 of 5: Using trigonometric & vectors) YT 18 minutes 34 seconds Eddie Woo Centre of a Major Arc (2 of 5: Finding centre and radius) YT 12 minutes 45 seconds Eddie Woo Centre of a Major Arc (1 of 5: Evaluating internal angle)

YT 8 minutes 8 seconds Eddie Woo How to graph a region on the complex plane YT 19 minutes 29 seconds Eddie Woo Three ways to find a parallelogram's area