For the whole question, calculator use is not allowed. Let the complex number $2 - i$ be called $u$.
(i)[4]
It is given that $u$ is a root of the equation $x^3 + ax^2 - 3x + b = 0$, where $a$ and $b$ are real constants. Find the values of $a$ and $b$.
(ii)[4]
On an Argand diagram, shade the set of points for complex numbers $z$ that satisfy both the inequalities $|z - u| < 1$ and $|z| < |z + i|$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Replace $x$ with $2-i$ or $2+i$ and try expanding” …
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