Factors 132022 By Chtan FYHSKulai 1 Functions of

Factors 1/3/2022 By Chtan FYHS-Kulai 1

Functions of the forms : Where n is positive integer. Can be expressed as products of real factors. Steps : 1. solve the corresponding equations. 2. combining pairs of linear complex factors. 1/3/2022 By Chtan FYHS-Kulai 2

(1) 1/3/2022 By Chtan FYHS-Kulai 3

ls ua Eq to Is closely related with the 1 st complex root 1/3/2022 By Chtan FYHS-Kulai 4

Similarly, the second last term 1/3/2022 By Chtan FYHS-Kulai 5

When n is even, there will be pairs of complex roots. There are 2 more roots 1 and -1. 1/3/2022 By Chtan FYHS-Kulai 6

When n is odd, there will be pairs of complex roots. There are 1 more root, the root 1. 1/3/2022 By Chtan FYHS-Kulai 7

Therefore, the pair of the complex roots such as lead to factors: 1/3/2022 By Chtan FYHS-Kulai 8

Hence, when n is even and > 2, 1/3/2022 By Chtan FYHS-Kulai 9

when n is odd and > 1, 1/3/2022 By Chtan FYHS-Kulai 10

(2) 1/3/2022 By Chtan FYHS-Kulai 11

Hence, when n is even and > 2, 1/3/2022 By Chtan FYHS-Kulai 12

when n is odd and > 1, 1/3/2022 By Chtan FYHS-Kulai 13

(3) 1/3/2022 By Chtan FYHS-Kulai 14

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forms the following quadratic factor similarly for other pairs. Hence, 1/3/2022 By Chtan FYHS-Kulai 16

e. g. 12 Express in real factors 1/3/2022 By Chtan FYHS-Kulai 17

Soln: 1/3/2022 (i) By Chtan FYHS-Kulai 18

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(ii) 1/3/2022 By Chtan FYHS-Kulai 20

Hence, 1/3/2022 By Chtan FYHS-Kulai 21

e. g. 13 Prove that Hence find 1/3/2022 By Chtan FYHS-Kulai 22

Expansions of Where n is positive integer 1/3/2022 By Chtan FYHS-Kulai 23

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e. g. 14 Show that Use your result to solve the equation 1/3/2022 By Chtan FYHS-Kulai 27

e. g. 15 Use De Moivre’s Theorem to find 1/3/2022 By Chtan FYHS-Kulai 28

Soln: 1/3/2022 By Chtan FYHS-Kulai 29

But , 1/3/2022 By Chtan FYHS-Kulai 30

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e. g. 16 1/3/2022 By Chtan FYHS-Kulai 32

e. g. 17 1/3/2022 By Chtan FYHS-Kulai 33

e. g. 18 1/3/2022 By Chtan FYHS-Kulai 34

e. g. 19 1/3/2022 By Chtan FYHS-Kulai 35

e. g. 20 Express in terms of multiple angles and hence evaluate 1/3/2022 By Chtan FYHS-Kulai 36

Soln: We have, (1) (2) 1/3/2022 By Chtan FYHS-Kulai 37

(1)x(2) 1/3/2022 By Chtan FYHS-Kulai 38

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e. g. 21 Express in terms of and hence evaluate terms of. 1/3/2022 By Chtan FYHS-Kulai in 43

The end 1/3/2022 By Chtan FYHS-Kulai 44