13 The Geometrical Effects of Multiplying by a Complex Number (scaling and rotation)

Multiplying by a complex number has the effect of scaling and rotating another complex number. Animations are given to illustrate this idea.
Detailed solutions of the following examples are given:
1. Describe the geometrical effect on a complex number z of multiplying z by:
(a) 1 + i (b) √2 - √2i (c) -1+ √3i
The viewer is encouraged to attempt these questions before watching the solutions.
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

Key words: Complex multiplication, scaling, origin, rotation, modulus, argument, principal value, π/3, π/4, π/2, cosø+isinø, Argand diagram,
M337, Open University, Unit A1, complex analysis