12 The Principal Argument of a Complex Number

This video discusses the idea of a Principal Value of the arguments of a complex number. There are many animated examples given to illustrate the idea.
The 2nd half of the video involves detailed solutions of the following examples:
1. Find the Principal Argument for each of these complex numbers:
(a) -1+√3i (b) -4 (c) 3i (d) -3-3i
2. For each of these complex numbers z, write down Arg z and express in polar form:
(a) -5i (b) 3√3-3i (c) -√3-i (d) -1+i
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

Key words: Principal Value, Principal Argument, complex number, polar form, modulus, argument, real part, imaginary part, Re(z), Im(z), a+ib, π/2, 3π/4, 1st quadrant, π, phi