20 De Moivre's Theorem Part 1 (Introduction & Visualisation)

Multiplication of two complex numbers in polar form is generalised to n complex numbers. A detailed solution to this example is given:
Use polar forms to evaluate the product of the complex numbers 1+ i, 1- i, 1+√3i and 1-√3i.
The particular case where the n complex numbers are identical is explored
using a GeoGebra animation of the Argand diagram.This lead to a statement of De Moivre's Theorem
Chapters:
00:00 Generalisation to n Complex Numbers
02:06 Example
02:16 Solution to Example
07:15 Particular case of n identical Complex Numbers
09:00 GeoGebra exploration (visualisation)
13:25 Statement of De Moivre's Theorem
15:20 Links to the Playlist "Complex Numbers"
Key words: modulus, argument, conjugate, polar form, Arg(z), GeoGebra, De Moivre's Theorem or Formula, 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