Mathematics 9709 · AS & A Level · Complex numbers

Complex numbers — practice question

(a)[2]

For the complex number $u = \frac{(\cos \frac{\pi}{7} + i \sin \frac{\pi}{7})^4}{\cos \frac{\pi}{7} - i \sin \frac{\pi}{7}}$, find the exact value of $\arg u$.

(b)[2]

On an Argand diagram, the complex numbers $u$ and $u^*$ are shown. Describe the one geometric transformation that sends $u$ to $u^*$ and state the exact value of $\arg u^*$.

Worked solution & mark scheme

This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: The arguments $\frac{4\pi}{7}$ and/or $-\frac{\pi}{7}$ are obtained

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