2025 RI Complex Numbers Assignment Q2

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

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

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

Find \(z\) and \(w\) in the form \(a+b\,\mathbf{i}\), where \(a\) and \(b\) are real, \(a\ne 0\).[5]