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Complex Numbers and Polynomials

Quick questions on De Moivre's theorem explained: H2 Further Mathematics

3short 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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State de Moivre's theorem for an integer power nn. [1 mark]
What is q2?
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Write z2+1z2z^2 + \dfrac{1}{z^2} in terms of a cosine, where z=cos⁡θ+isin⁡θz = \cos\theta + i\sin\theta. [1 mark]
What is q3?
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Using the expansion of (cos⁡θ+isin⁡θ)2(\cos\theta + i\sin\theta)^2, find cos⁡2θ\cos 2\theta in terms of cos⁡θ\cos\theta. [2 marks]

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