How Complex Numbers fit with other Numbers
Example 1
Example 1 Video
Example 2
Example 2 Video
Example 3
Example 3 Video
Geometric Explanation of i
Real World Uses of Complex Numbers
The Complex Plane
Powers of i
Example 4
Example 4 Video
Example 5
Example 5 Video
Exercise 2.1
Exercise 2.1 Recorded Solutions
Forms of a Complex Number
Example 1
Example 1 Video
Example 2
Example 2 Video
Example 3
Example 3 Video
Conjugate of a Complex Number
Example 4
Example 4 Video
Example 5
Example 5 Video
Example 6
Example 6 Video
Example 7
Example 7 Video
Exercise 2.2
Exercise 2.2 Recorded Solutions
Modulus, Argument and Mod-arg Form
Example 1
Example 1 Video
Example 2
Example 2 Video
Multiplying Complex Numbers in Mod-Arg Form
Example 3
Example 3 Video
Division of Complex Numbers in Mod-Arg Form
Example 4
Example 4 Video
Conjugate in Mod-Arg Form
Example 5
Example 5 Video
Exercise 2.3
Exercise 2.3 Recorded Solutions
Exponential Form
Euler's Formula
Understanding Exponential Form
Proving Euler’s Formula
Proof 1
Proof 1 Video
Euler’s Identity
Proof 2
Proof 2 Video
Example 3
Example 3 Video
Calculations in Exponential Form
Example 4
Example 4 Video
Example 5
Example 5 Video
Exponential Form
Example 6
Example 6 Video
Compare and Convert Between Forms
Example 7
Example 7 Video
Exercise 2.4
Exercise 2.4 Recorded Solutions
Method 1 - Simultaneous Equations
Example 1
Example 1 Video
Method 1a - Simultaneous Equations (Shortcut Method)
Example 2
Example 2 Video
Example 3
Example 3 Video
Method 2 - Formula
Example 4
Example 4 Video
Example 5
Example 5 Video
Exercise 2.5
Exercise 2.5 Recorded Solutions
Product of Conjugates
Example 1
Example 1 Video
Reciprocal of z and its conjugate
Example 2
Example 2 Video
Sum of Conjugates
Example 3
Example 3 Video
Example 4
Example 4 Video
Example 5
Example 5 Video
Difference of Conjugates
Example 6
Example 6 Video
Example 7
Example 7 Video
Operations with Conjugates
Example 8
Example 8 Video
Conjugate Root Theorem
Example 9
Example 9 Video
Exercise 2.6
Exercise 2.6 Recorded Solutions
Complex Numbers as Vectors
Triangle and Parallelogram Laws (Adding Vectors)
Subtracting Vectors
Polygon Law (Adding Vectors)
Example 1
Example 1 Video
Rotation and Dilation
Parallel Vectors
Example 2
Example 2 Video
Perpendicular Vectors
Example 3
Example 3 Video
Rotating by alpha
Example 4
Example 4 Video
Midpoint
Example 5
Example 5 Video
Triangle Inequality
Example 6
Example 6 Video
Exercise 2.7
Exercise 2.7 Recorded Solutions
Curves and Regions
Circles
Example 1
Example 1 Video
Perpendicular Bisector
Example 2
Example 2 Video
Rays and Sectors
Example 3
Example 3 Video
Example 4 (Horizontal and Vertical Lines)
Example 4 Video
Example 5 (Algebraic Method)
Example 5 Video
Arcs
Example 6
Example 6 Video
Exercise 2.8
Exercise 2.8 Recorded Solutions
De Moivre’s Theorem
Example 1
Example 1 Video
Example 2
Example 2 Video
Trigonometrical Applications of De Moivre’s Theorem
Example 3
Example 3 Video
Example 4
Example 4 Video
Solving Equations with Trigonometric Identities
Example 5
Example 5 Video
Exercise 2.9
Exercise 2.9 Recorded Solutions
Complex Roots of Unity
Example 1
Example 1 Video
Example 2
Example 2 Video
Some points to note before we continue
Example 3
Example 3 Video
Complex Roots of -1
Example 4
Example 4 Video
Roots of Other Complex Numbers
Example 5
Example 5 Video
Example 6
Example 6 Video
Exercise 2.10
Exercise 2.10 Recorded Solutions
Steve Howard