Question 19 - A-Level Maths

Exam Board	Edexcel
Module	FP1 (Further Pure Mathematics 1)
Topic	Complex Numbers Arithmetic
Type	Multi-part questions with division as one step

Given that \(z = 1 + \sqrt { } 3 \mathrm { i }\) and that \(\frac { w } { z } = 2 + 2 \mathrm { i }\), find
1. \(w\) in the form \(a + \mathrm { i } b\), where \(a , b \in \mathbb { R }\),
2. the argument of \(w\),
3. the exact value for the modulus of \(w\).
On an Argand diagram, the point \(A\) represents \(z\) and the point \(B\) represents \(w\).
Draw the Argand diagram, showing the points \(A\) and \(B\).
Find the distance \(A B\), giving your answer as a simplified surd.