2:39
Someone asked me a question about Euler's Identity (e^iπ = --1)...
Eddie Woo
12:56
Polynomials w/ Complex Roots (interesting exam question)
9:55
Exam Problem: Cubic Polynomial w/ 1 Real Root
9:10
Introduction to Complex Numbers (1 of 2: The Backstory)
9:53
Complex Arithmetic (1 of 2: Addition & Multiplication)
8:55
Complex Arithmetic (2 of 2: Conjugates & Division)
11:13
Introduction to Complex Numbers (2 of 2: Why Algebra Requires Complex Numbers)
13:53
Who cares about complex numbers??
5:06
Linear Factorisation of Polynomials (1 of 2: Working in the Complex Field)
4:56
Square Roots of Complex Numbers (1 of 2: Establishing their nature)
12:22
Square Roots of Complex Numbers (2 of 2: Introductory example)
7:02
Linear Factorisation of Polynomials (2 of 2: Introductory example)
9:04
Complex Numbers - Mod-Arg Form (1 of 5: Introduction)
8:33
Complex Numbers - Mod-Arg Form (2 of 5: Visualising Modulus & Argument)
6:44
Complex Numbers - Mod-Arg Form (3 of 5: Calculating the Modulus)
6:13
Complex Numbers - Mod-Arg Form (4 of 5: Conversion Example 1)
7:57
Complex Numbers - Mod-Arg Form (5 of 5: Conversion Example 2)
8:22
Multiplying Complex Numbers in Mod-Arg Form (1 of 2: Reconsidering powers of i)
6:54
Multiplying Complex Numbers in Mod-Arg Form (2 of 2: Generalising the pattern)
9:57
Relationships Between Moduli & Arguments in Products of Complex Numbers
7:34
Powers of a Complex Number (example question)
6:07
Understanding Complex Quotients & Conjugates in Mod-Arg Form
11:43
Manipulating Complex Numbers for Purely Real Results
12:43
Complex Numbers Question (Finding the greatest value of |z| if |z-4/z|=2)
11:01
Complex Conjugate Root Theorem (Formal Proof)
9:27
Complex Conjugate Root Theorem (1 of 2: Using the Conjugate Root Theorem to solve Polynomials)
5:05
Complex Conjugate Root Theorem (2 of 2: Alternatively solving with Long Division)
10:38
Extension II Assessment Review (1 of 5: Multiple Choice Questions Section)
5:39
Extension II Assessment Review (2 of 5: Complex Conjugate Root Theorem, DMT & Geometry)
11:36
The Most Beautiful Identity (1 of 8: Introducing Complex Numbers)
6:33
The Most Beautiful Identity (2 of 8: Same number, different clothes)
7:27
The Most Beautiful Identity (3 of 8: The Complex Plane)
8:03
The Most Beautiful Identity (4 of 8: Polar Form)
7:13
The Most Beautiful Identity (5 of 8: Polynomial Interpolation)
9:08
The Most Beautiful Identity (6 of 8: Taylor Series)
6:32
The Most Beautiful Identity (7 of 8: Revisiting Polar Form)
10:56
The Most Beautiful Identity (8 of 8: Conclusion)
10:42
Square Roots of Complex Numbers
5:21
Why √a√b isn't always equal to √ab
5:02
Geometry of Complex Numbers (1 of 6: Radians)
6:51
Geometry of Complex Numbers (2 of 6: Real vs. Complex)
11:06
Geometry of Complex Numbers (3 of 6: Real Arithmetic)
5:32
Geometry of Complex Numbers (4 of 6: The Complex Plane)
12:40
Geometry of Complex Numbers (5 of 6: Polar Form)
6:43
Geometry of Complex Numbers (6 of 6: Conversion Between Forms)
12:49
Polar Form (1 of 2: Using Complex Number examples to justify polar form's use)
10:48
Polar Form (2 of 2: Generalising to prove the multiplication identity of polar form)
7:41
Parallelogram Law (Geometrically representing the addition of complex numbers with vectors)
10:08
Solutions of (1+i)z² - z - i = 0
9:47
Graphing with Complex Numbers (1 of 3: Initial algebraic expansion)
7:14
Graphing with Complex Numbers (2 of 3: Determining the region)
12:46
Graphing with Complex Numbers (3 of 3: Is |z₁z₂| equal to |z₁| × |z₂|?)
12:37
Introducing Complex Numbers (1 of 3: History of numbers)
Introducing Complex Numbers (2 of 3: Revealing the invisible)
8:27
Introducing Complex Numbers (3 of 3: Defining fundamentals)
14:56
Complex Arithmetic (1 of 3: Basic operations)
12:13
Complex Arithmetic (2 of 3: Trigonometric identity)
9:19
Complex Arithmetic (3 of 3: Identity from ℝ component)
10:09
Further Complex Arithmetic (1 of 2: Basic questions and notation)
10:05
Further Complex Arithmetic (2 of 2: Equating components)
8:31
Introducing the Complex Plane
12:19
Exploring the Complex Plane (1 of 2: Visualising addition & subtraction)
15:28
Exploring the Complex Plane (2 of 2: Visualising multiplication)
12:00
Basics of Complex Geometry (example questions)
10:53
Introducing Polar Form (1 of 3: An alternative coordinate system)
9:32
Introducing Polar Form (2 of 3: Relationship to rectangular form)
11:12
Introducing Polar Form (3 of 3: Example conversion)
14:02
Working in Polar Form (1 of 2: Conjugate & negative)
15:26
Working in Polar Form (2 of 2: Square & reciprocal)
4:48
Distance between complex numbers
19:05
Exact value of cos(π÷12)
9:56
Quotient of Complex Numbers (1 of 2: Evaluating modulus)
11:31
Quotient of Complex Numbers (2 of 2: Evaluating argument)
15:18
Working with Moduli and Arguments (Proof Question)
Argument of the Complex Conjugate
10:29
Square Roots of a Complex Number (3 of 3: Solving in rectangular and exponential form)
9:24
Square Roots of a Complex Number (2 of 3: Principal square root)
7:04
Square Roots of a Complex Number (1 of 3: Review questions)
Proving Euler's Formula (4 of 4: Evaluating constants)
10:20
Proving Euler's Formula (3 of 4: Equating terms)
11:59
Proving Euler's Formula (2 of 4: Differentiating both sides)
11:04
Proving Euler's Formula (1 of 4: Fields)
8:15
What does an imaginary power mean?
10:50
Informal Proof of Euler's Formula (2 of 2: Trigonometric calculus)
15:21
Informal Proof of Euler's Formula (1 of 2: Exponential calculus)
