Chapter 10: Further Core Pure 2: Complex Numbers

A-level Further MathsFurther Core Pure7 topicsHigher

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Further Core Pure 2: De Moivre's Theorem Long-Answer Questions

Examiner-style long-answer practice with automatic marking, improvement advice and ProofCoach tracking.

4 questions24 marks36 min

standard / hard / synoptic

6 marksfindstandardEdexcel

FCP10-1: (cos

\theta

+ i sin

theta)^{4}

. Find cos 4theta + i sin 4theta for De Moivre's theorem and trigonometric identities. Show the method clearly by using apply De Moivre's theorem for integer powers.

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6 marksshow thatstandardEdexcel

FCP10-2 verification: show that the printed answer is valid by applying apply De Moivre's theorem for integer powers. Include a check using (cos

\theta

+ i sin

theta)^{4}

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6 marksprovehardEdexcel

FCP10-3 proof: starting with (cos

\theta

+ i sin

theta)^{4}

, prove cos 4theta + i sin 4theta for De Moivre's theorem and trigonometric identities; give restrictions.

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6 markshencesynopticEdexcel

Using FCP10-4's earlier result cos 4theta + i sin 4theta, hence solve the linked problem in De Moivre's theorem and trigonometric identities and state whether the answer is exact or rounded.

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9. Further Core Pure 1: Vectors

11. Further Core Pure 2: Series

Key learning objectives

Understand the key principles behind Further Core Pure 2: Complex Numbers.
Apply these ideas to exam-style questions.
Recall the essential definitions and key terms.