2024 MI PRU2 P2 Q1

Do not use a calculator in answering this question.

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

\(2w+\mathbf{i}\,z=1\)
\({{w}^{*}}+2z=7+11\,\mathbf{i}\)

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