(a)[3]
Find a simplified form of $f(a)$ in terms of $y$.
(b)[3]
Given that $\operatorname{Re}(f(a)) = -20$, determine $a$.
Mathematics 9709 · AS & A Level · Complex numbers
Complex numbers — practice question
The complex number $2 + yi$ is represented by $a$, with $y$ being a real number and $y < 0$. It is stated that $f(a) = a^3 - a^2 - 2a$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “After substituting $2+yi$ into $a^3-a^2-2a$, work out $a^2$ and $a^3$.” …
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