<p><strong>Do not use a calculator in answering this question.</strong></p>
<p>The point $P$ represents the complex number $z=-2+b\,\mathbf{i}$, where $b>0$. The line $OP$ makes an angle of ${{45}^{{}^\circ }}$ with the horizontal.</p>
<ol class="i-list"><li><div class="list-item-paragraph">State the value of $b$.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">Hence find the modulus and argument of $\frac{1}{z}$.</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">Show on an Argand diagram the points $P$, $Q$ and $R$ representing the complex numbers $z$, $\frac{1}{z}$ and $z+\frac{1}{z}$ respectively. Indicate on your diagram the value of $\angle PRQ$.</div><p style="text-align: right;">[3]</p></li></ol>

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

The point $P$ represents the complex number $z=-2+b\,\mathbf{i}$, where $b>0$. The line $OP$ makes an angle of ${{45}^{{}^\circ }}$ with the horizontal.

Hence find the modulus and argument of $\frac{1}{z}$.

Show on an Argand diagram the points $P$, $Q$ and $R$ representing the complex numbers $z$, $\frac{1}{z}$ and $z+\frac{1}{z}$ respectively. Indicate on your diagram the value of $\angle PRQ$.

2021 ASRJC JC2 MYA P1 Q3

2021 ASRJC JC2 MYA P1 Q3

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