17 Division of Complex Numbers in Polar Form
Dividing two complex numbers involves dividing their moduli and subtracting their arguments. An animation (using GeoGebra) is used to illustrate these ideas.
Detailed solutions of the following examples are given:
1. Use polar forms to show that i/-i = -1
2. For z=1 and w=1-i use polar forms to evaluate z/w.
3. Let z=-1+√3i and w=-√3-i
(a) Give the polar forms of z and w.
(b) Use your part (a) answer to evaluate z/w.
(c) Obtain your part (b) answer without using polar forms.
The viewer is encouraged to attempt these questions before watching the solutions.
Chapters:
00:00 Introductory animation
04:52 Mathematical derivation of results
08:55 The examples
09:09 Solution to Example 1
11:55 Solution to Example 2
15:11 Solution to Example 3
23:58 Links to the Playlist "Complex Numbers"
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
Key words: Complex division, modulus, argument, difference, subtraction, division, conjugate, principal value, Arg(z), polar form, cartesian form.
M337, Open University, Unit A1, complex analysis