2017 HCI P2 Q2

The complex numbers \(z\) and \(w\) satisfy the following equations

\(2z+3w=20\),

\(w-z{{w}^{*}}=6+22\mathbf{i}\).

1. Find \(z\) and \(w\) in the form \(a+b\mathbf{i}\), where \(a\) and \(b\) are real, \(a\ne 0\).[5]
2. Show \(z\) and \(w\) on a single Argand diagram, indicating clearly their modulus. State the relationship between \(z\) and \(w\) with reference to the origin \(O\).[2]