<p><strong>Do not use a calculator in answering this question.</strong></p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Given that&nbsp;$x=1+3\mathbf{i}$ is a root of the equation $x^3 + ax^2 + 18x + b = 0$, find the values of the real numbers $a$ and $b$, and the other roots.</span><span class="inline-marks">[5]</span></div></li><li><div class="list-item-content"><span class="list-item-text">The complex numbers $z$ and $w$ satisfy the following equations.</span></div></li></ol>
<p style="text-align: center">$w^* + z = 4 - 6\mathbf{i}$<br>$w - 2z = 1 + 10\mathbf{i}$</p>
<p>Find $z$ and $w$, giving your answers in the form $c + \mathbf{i}d$, where&nbsp;$c$ and $d$ are real numbers.<span class="inline-marks">[5]</span></p>

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

Given that $x=1+3\mathbf{i}$ is a root of the equation $x^3 + ax^2 + 18x + b = 0$, find the values of the real numbers $a$ and $b$, and the other roots.

The complex numbers $z$ and $w$ satisfy the following equations.

$w^* + z = 4 - 6\mathbf{i}$
$w - 2z = 1 + 10\mathbf{i}$

Find $z$ and $w$, giving your answers in the form $c + \mathbf{i}d$, where $c$ and $d$ are real numbers.

2024 RI Promo Q7

2024 RI Promo Q7