Question 6 - A-Level Maths

Given that \(z = 3 + 4 \mathrm { i }\) and \(w = - 1 + 7 \mathrm { i }\),
1. find \(| w |\).
The complex numbers \(z\) and \(w\) are represented by the points \(A\) and \(B\) on an Argand diagram.
Show points \(A\) and \(B\) on an Argand diagram.
Prove that \(\triangle O A B\) is an isosceles right-angled triangle.
Find the exact value of \(\arg \left( \frac { z } { w } \right)\).