<p><strong>Do not use a calculator in answering this question.</strong></p>
<p>The complex number \(w\) is such that \(w=\mathrm{i}-\sqrt{3}\).</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find \(|w|\) and \(\mathrm{arg}(w)\) in exact form.</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Represent \(w\), \(-w\) and \(2-w\) in the same Argand diagram, illustrating clearly the geometrical relationship between them.</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Hence, find \(\mathrm{arg}(2-w)\) exactly.</span><span class="inline-marks">[2]</span></div></li></ol>

**Do not use a calculator in answering this question.**

The complex number \(w\) is such that \(w=\mathrm{i}-\sqrt{3}\).

Find \(|w|\) and \(\mathrm{arg}(w)\) in exact form.

Represent \(w\), \(-w\) and \(2-w\) in the same Argand diagram, illustrating clearly the geometrical relationship between them.

2025 NJC P2 Q1

2025 NJC P2 Q1