21 De Moivre's Theorem Part 2 (proof for all Integers)

The proof of De Moivre's Theorem for all Integers (positive, negative and zero) is given. The three steps are: Mathematical Induction for the positive integers, the case n=0 and then the proof for the negative integers which involves the reciprocal.
The analogy of falling dominoes is used to help understand the inductive process.
Chapters:
00:10 Statement of the Theorem and Proof strategy
01:09 Step 1: animation of domino analogy
02:08 Step 1: proof by Mathematical Induction for the positive integers
06:11 Step 2: the case n=0
07:50 Step 3: proof for the negative integers by use of the reciprocal
11:42 The summary
12:00 Links to the Playlist "Complex Numbers"
Key words: De Moivre's Theorem, Mathematical Induction, Z+, Z-, Z, reciprocal, indices, arguments, M337, Open University, Unit A1, complex analysis

Previous videos in this series are:
01 What is a Complex Number?
02 Adding, Subtracting and Multiplying Complex Numbers
03 Dividing Complex Numbers
04 Complex Conjugates
05 The Field of Complex Numbers
06 The Complex Plane
07 The Modulus of a Complex Number
08 Distance on the Complex Plane
09 Properties of the Modulus of a Complex Number
10 Complex Numbers and the Unit Circle
11 The Polar Form of a Complex Number
12 The Principal Argument of a Complex Number
13 The Geometrical Effects of Multiplying by a Complex Number
14 Multiplication of Complex Numbers in Polar Form
15 The Principal Argument when Multiplying Complex Numbers
16 The Geometrical Effects of Dividing by a Complex Number
17 Division of Complex Numbers in Polar Form
18 Properties of the Reciprocal of a Complex Numbers
19 Conjugates and Reciprocals of Complex Numbers
20 De Moivre's Theorem Part 1 (Introduction & Visualisation)