What I personally think the reason for the principal argument to be restricted between -pi and pi is because of the ease of multiplication. When we multiply two or more complex numbers they elongate by the combined (product) modulus and rotate by the combined (sum) argument . The disjoint interval given for the principal argument helps if multiplication was considered as a transformation such that the product measures as 1+ 0i in the transformed coordinate system. When there are multiple complex numbers in the same argand plane this basis transformation could be helpfull. Some problems in physics are solved in such a way. Hope this helps.
What I personally think the reason for the principal argument to be restricted between -pi and pi is because of the ease of multiplication. When we multiply two or more complex numbers they elongate by the combined (product) modulus and rotate by the combined (sum) argument . The disjoint interval given for the principal argument helps if multiplication was considered as a transformation such that the product measures as 1+ 0i in the transformed coordinate system. When there are multiple complex numbers in the same argand plane this basis transformation could be helpfull. Some problems in physics are solved in such a way. Hope this helps.
Unambiguous also happens to be a smaller angle of rotation, just in the other direction.
Will you be making videos for the new syllabus maths?
Fucking Legend