Complex Numbers

Introduction to Complex Numbers (1 of 2: The Backstory).
Introduction to Complex Numbers (2 of 2: Why Algebra Requires Complex Numbers).
Who cares about complex numbers??.
Why Complex Numbers? (1 of 5: Atoms & Strings).
Why Complex Numbers? (2 of 5: Impossible Roots).
Why Complex Numbers? (3 of 5: The Imaginary Unit).
Why Complex Numbers? (4 of 5: Turning the key).
Why Complex Numbers? (5 of 5: Where to now?).
Complex Arithmetic (1 of 2: Addition & Multiplication).
Complex Arithmetic (2 of 2: Conjugates & Division).
Square Roots of Complex Numbers (1 of 2: Establishing their nature).
Square Roots of Complex Numbers (2 of 2: Introductory example).
Linear Factorisation of Polynomials (1 of 2: Working in the Complex Field).
Linear Factorisation of Polynomials (2 of 2: Introductory example).
Manipulating Complex Numbers for Purely Real Results.
Powers of a Complex Number (example question).
Complex Numbers as Vectors (1 of 3: Introduction & Addition).
Complex Numbers as Vectors (2 of 3: Subtraction).
Complex Numbers as Vectors (3 of 3: Using Geometric Properties).
Vectors (1 of 4: Outline of vectors and their ability to represent complex number).
Vectors (2 of 4: Representing addition & subtraction of complex numbers with vectors).
Vectors (3 of 4: Geometrically representing multiplication of complex numbers with vectors).
Vectors (4 of 4: Outlining the usefulness of vectors in representing geometry).
Complex Numbers - Mod-Arg Form (1 of 5: Introduction).
Complex Numbers - Mod-Arg Form (2 of 5: Visualising Modulus & Argument).
Complex Numbers - Mod-Arg Form (3 of 5: Calculating the Modulus).
Complex Numbers - Mod-Arg Form (4 of 5: Conversion Example 1).
Complex Numbers - Mod-Arg Form (5 of 5: Conversion Example 2).
Multiplying Complex Numbers in Mod-Arg Form (1 of 2: Reconsidering powers of i).
Multiplying Complex Numbers in Mod-Arg Form (2 of 2: Generalising the pattern).
Relationships Between Moduli & Arguments in Products of Complex Numbers.
De Moivre's Theorem.
How to graph the locus of |z-1|=1.
Understanding Complex Quotients & Conjugates in Mod-Arg Form.
Complex Numbers as Points (1 of 4: Geometric Meaning of Addition).
Complex Numbers as Points (2 of 4: Geometric Meaning of Subtraction).
Complex Numbers as Points (3 of 4: Geometric Meaning of Multiplication).
Complex Numbers as Points (4 of 4: Second Multiplication Example).
Introduction to Radians (1 of 3: Thinking about degrees).
Introduction to Radians (2 of 3: Defining a better way).
Introduction to Radians (3 of 3: Definition + Why Radians Aren't Units).
Complex Roots (1 of 5: Introduction).
Complex Roots (2 of 5: Expanding in Rectangular Form).
Complex Roots (3 of 5: Through Polar Form Using De Moivre's Theorem).
Complex Roots (4 of 5: Through Polar Form Generating Solutions).
Complex Roots (5 of 5: Flowing Example - Solving z^6=64).
Using Inverse tan to find arguments? (1 of 2: Why it doesn't work... Sometimes).
Using Inverse tan to find arguments? (2 of 2: Why it works... Sometimes).
Graphs on the Complex Plane [Continued] (1 of 4: What's behind the graph?).
Graphs on the Complex Plane [Continued] (2 of 4: Finding Regions of Inequality by Testing Points).
Graphs on the Complex Plane (3 of 4: Geometry of arg(z)-arg(z-1)).
Graphs on the Complex Plane (4 of 4: Exploring how the argument traced the graph).
Further Graphs on the Complex Plane (1 of 3: Geometrical Representation of Moduli).
Further Graphs on the Complex Plane (2 of 3: Algebraically verifying Graphs concerning the Moduli).
Further Graphs on the Complex Plane (3 of 3: Geometrical Representation of Arguments).
Graphs in the Complex Plane (1 of 4: Introductory Examples).
Graphs in the Complex Plane (2 of 4: Graphing Complex Inequalities).
Graphs in the Complex Plane (3 of 4 : Shifting the Point of Reference).
Graphs in the Complex Plane (4 of 4: Where is the argument measured from?).
The Triangle Inequalities (1 of 3: Sum of Complex Numbers).
The Triangle Inequalities (2 of 3: Discussing Specific Cases).
The Triangle Inequalities (3 of 3: Difference of Complex Numbers).
DMT and Trig Identities (1 of 4: Deriving multi-angle identities with compound angles).
DMT and Trig Identities (2 of 4: Using De Moivre's Theorem and Binomial Expansions).
DMT and Trig Identities (3 of 4: Deriving tan expression from cos and sin).
DMT and Trig Identities (4 of 4: Using Multi-angle formula to solve polynomials).
Complex Conjugate Root Theorem (1 of 4: Using DMT and Polar Form to solve for Complex Roots).
Complex Conjugate Root Theorem (2 of 4: Introduction to the Conjugate Root Theorem).
Complex Conjugate Root Theorem (3 of 4: Geometrical Shape represented by Conjugate Root Theorem).
Complex Conjugate Root Theorem (4 of 4: Using Factorisation to find patterns with Roots of Unity).
Complex Numbers (1 of 6: Solving Harder Complex Numbers Questions) [Student requested problem].
Complex Numbers (2 of 6: Solving Harder Complex Numbers Questions) [Student Requested Problem].
Complex Numbers (3 of 6: Harder Complex Numbers Question) [Student Requested Problem].
Complex Numbers (4 of 6: Harder Complex Numbers Questions) [Student Requested Problem].
Complex Numbers (5 of 6: Complex Numbers Proofs [Using the Conjugate]).
Complex Numbers (6 of 6: Finishing off the Proof).
2016 HSC - Complex Numbers on Unit Circle (1 of 2: Considering Re & Im Parts).
2016 HSC - Complex Numbers on Unit Circle (2 of 2: Evaluating the arguments).
2016 HSC - Complex Identity Proof (1 of 3: Convert to polar form).
2016 HSC - Complex Identity Proof (2 of 3: Using binomial theorem).
2016 HSC - Complex Identity Proof (3 of 3: Combining results).
Complex Numbers Question (Finding the greatest value of |z| if |z-4/z|=2).
Argand Diagram / Locus Question.
The Most Beautiful Identity (1 of 8: Introducing Complex Numbers).
The Most Beautiful Identity (2 of 8: Same number, different clothes).
The Most Beautiful Identity (3 of 8: The Complex Plane).
The Most Beautiful Identity (4 of 8: Polar Form).
The Most Beautiful Identity (5 of 8: Polynomial Interpolation).
The Most Beautiful Identity (6 of 8: Taylor Series).
The Most Beautiful Identity (7 of 8: Revisiting Polar Form).
The Most Beautiful Identity (8 of 8: Conclusion).
Geometry of Complex Numbers (1 of 6: Radians).
Geometry of Complex Numbers (2 of 6: Real vs. Complex).
Geometry of Complex Numbers (3 of 6: Real Arithmetic).
Geometry of Complex Numbers (4 of 6: The Complex Plane).
Geometry of Complex Numbers (5 of 6: Polar Form).
Geometry of Complex Numbers (6 of 6: Conversion Between Forms).
Graphing with Complex Numbers (1 of 3: Initial algebraic expansion).
Graphing with Complex Numbers (2 of 3: Determining the region).
Graphing with Complex Numbers (3 of 3: Is |z₁z₂| equal to |z₁| × |z₂|?).
Curves and Regions on the Complex Plane (1 of 4: Introductory example plotting |z|=5 geometrically).
Curves and Regions on the Complex Plane (2 of 4: Deciphering terminology to plot complex numbers).
Curves and Regions on the Complex Plane (3 of 4: Simplifying expressions to plot on a complex plane).
Curves and Regions on the Complex Plane (4 of 4: Plotting simultaneous shifted complex numbers).
Parallelogram Law (Geometrically representing the addition of complex numbers with vectors).
Complex Conjugate Root Theorem (Formal Proof).
Complex Roots (1 of 5: Observing Complex Conjugate Root Theorem through seventh roots of unity).
Complex Roots (2 of 5: Using Trigonometrical Identities & Conjugates to solve an equation).
Complex Roots (3 of 5: Using DMT to solve an equation of roots of unity).
Complex Roots (4 of 5: Using Polynomial Identities to prove unity identities).
Complex Roots (5 of 5: Using Geometric Progression to find factors of ω^n - 1).
Square Roots of Complex Numbers.
Polynomials w/ Complex Roots (interesting exam question).
Interesting Complex Polynomial Question (1 of 2: Factorisation).
Interesting Complex Polynomial Question (2 of 2: Trigonometric Result).