| Exam Board | WJEC |
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| Module | Further Unit 4 (Further Unit 4) |
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| Year | 2023 |
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| Session | June |
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| Topic | Complex numbers 2 |
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3. (a) Given that \(z = \cos \theta + \operatorname { isin } \theta\), use de Moivre's theorem to show that
$$z ^ { n } + \frac { 1 } { z ^ { n } } = 2 \cos n \theta$$
(b) Express \(32 \cos ^ { 6 } \theta\) in the form \(a \cos 6 \theta + b \cos 4 \theta + c \cos 2 \theta + d\), where \(a , b , c , d\) are integers whose values are to be determined.