<p>The complex numbers \(z\) and \(w\) satisfy the simultaneous equations \(\vert{}z\vert{} - w^* = -3 - \sqrt{2}\mathrm{i}\) and \(w^* + w + 5z = 1 + 20\mathrm{i}\), where&nbsp;\(w^*\) is the complex conjugate of \(w\). Find the value of \(z\) and the corresponding value of \(w\).<span class="inline-marks">[4]</span></p>

The complex numbers \(z\) and \(w\) satisfy the simultaneous equations \(\vert{}z\vert{} - w^* = -3 - \sqrt{2}\mathrm{i}\) and \(w^* + w + 5z = 1 + 20\mathrm{i}\), where \(w^*\) is the complex conjugate of \(w\). Find the value of \(z\) and the corresponding value of \(w\).

Complex Numbers

Complex Numbers