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