Quick questions on De Moivre's theorem: powers, the exponential form, identities and nth roots - CCEA A-Level Further Maths

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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Use de Moivre to find

\left(\cos\frac{\pi}{6} + i\sin\frac{\pi}{6}\right)^3

. [2 marks]

What is q2?

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How many distinct

n

th roots does a non-zero complex number have? [1 mark]

What is q3?

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Write

z = 2e^{i\pi/3}

in the form

r(\cos\theta + i\sin\theta)

. [1 mark]

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