2023 CJC P1 Q1

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

\(2z+1=\left| w \right|\)

\(2w-z=4+24\,\mathbf{i}\)

Find \(z\) and \(w\), giving your answers in the form \(a+\mathbf{i}\,b\) where \(~a\) and \(b\) are real numbers.[4]