11 The Polar Form of a Complex Number

This video extends the polar form representation of complex numbers on the unit circle (as covered in Video 10 of this series) to that of any complex number on the Complex Plane.
Illustrations are given of how the geometry of complex number is underpinned by the associated vector geometry. Examples are illustrated using addition and subtraction of complex numbers. Scaling of associated vectors is then used (i.e. multiplication of a vector by a real number scale factor) to generalise the polar form result for complex numbers on the unit circle (i.e. complex numbers with modulus of 1)
The 2nd half of the video involve detailed solutions of the following examples:
1. Represent -2 - i in polar form in two different ways
2.(a) Represent the complex number 3i in polar form
(b) Find a polar representation for -1 + i
(c) Represent the complex number 2√2(cos(-π/4) + i sin(-π/4)) in cartesian form
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

Key words: complex number, polar form, cartesian form, modulus, argument. associated vector, vector addition, negative of a vector, vector subtraction, vector scaling, scale factor, enlargement, reduction, dilatation, complex geometry, real part, imaginary part, Re(z), Im(z), a+ib, π/2, 3π/4