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