2025 NJC P1 Q2

Do not use a calculator in answering this question.

1. Find the values of \(z\) and \(w\) that satisfy the equations \((1+\mathrm{i})z + 2w = -2 + 4\mathrm{i}\) and \(3z - w = 4 + 2\mathrm{i}\), expressing your answers in the form \(c + d\mathrm{i}\), where \(c, d \in \mathbb{R}\).[4]
2. Points \(W\) and \(Z\) represent \(w\) and \(z\) found in part (i). Find \(\frac{w}{z}\) in the form \(p + \mathrm{i}q\), where \(p, q \in \mathbb{R}\). Hence, state the transformation that maps line segment \(OZ\) onto line segment \(OW\).[2]