N2026 P1 Q5

Do not use a calculator in answering this question.

Find the complex numbers \(z\) and \(w\) which satisfy these simultaneous equations.

\[\begin{gathered} 2z+7\mathrm{i}=-\mathrm{i}w\\ z-4=w-4\mathrm{i} \end{gathered}\]

Give your answers in the form \(a+\mathrm{i}b\), where \(a\) and \(b\) are real numbers.[5]