(i)[5]
a representation of $z$ in the form $re^{i\theta}$, where $r > 0$ and $-\pi < \theta \leq \pi$.
(ii)[3]
the two square roots of $z$, with answers written in the form $re^{i\theta}$, where $r > 0$ and $-\pi < \theta \leq \pi$.
Mathematics 9709 · AS & A Level · Complex numbers
Complex numbers — practice question
The complex number $z$ is specified by $z = \frac{9\sqrt{3} + 9i}{\sqrt{3} - i}$. Find, showing all your working,
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Multiply the numerator and the denominator by $\sqrt{3}+i$ and use $i^2=-1$” …
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