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Core Pure: complex numbers

Quick questions on De Moivre's theorem: powers, multiple-angle identities and powers of sine and cosine - OCR A-Level Further Maths A

2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is q1?
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Use de Moivre to evaluate (cos⁡π6+isin⁡π6)6\left(\cos\tfrac{\pi}{6} + i\sin\tfrac{\pi}{6}\right)^6. [2 marks]
What is q2?
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State the real and imaginary parts you would equate to derive cos⁡4θ\cos 4\theta from (cos⁡θ+isin⁡θ)4(\cos\theta + i\sin\theta)^4. [2 marks]

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