Mathematics 9709 · AS & A Level · Complex numbers

Complex numbers — practice question

The complex number $u$ is defined by $u = -1 - i\sqrt{3}$.
(a)[2]

Write $u$ in the form $r(\cos \theta + i\sin \theta)$, where $r > 0$ and $-\pi < \theta \leq \pi$. State the exact values of $r$ and $\theta$.

(b)[2]

The complex number $v$ is given by $v = 5\left(\cos \frac{\pi}{6} + i\sin \frac{\pi}{6}\right)$. Write the complex number $\frac{v}{u}$ in the form $re^{i\theta}$ where $r > 0$ and $-\pi < \theta \leq \pi$.

Worked solution & mark scheme

This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: Indicate or deduce $r=2$

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