(a) Given w = √3-i, (i) express w in polar form. (ii) find all the roots of 25 = √3-i in polar form. Show all the roots on an Argand diagram. (b) Use de Moivre's theorem to show that cos 50 = 16 cos5 - 20 cos³ 0+5 cos 0. Hence, solve 32r³-402³ + 10x = √√3.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(a) Given w = √3 - i,
(i) express w in polar form.
(ii) find all the roots of 25 = √3-i in polar form. Show all the roots
on an Argand diagram.
(b) Use de Moivre's theorem to show that
cos 50 = 16 cos 0 - 20 cos³0+5 cos 0.
Hence, solve 32r5 - 40x³ + 10x =
√3.
Transcribed Image Text:(a) Given w = √3 - i, (i) express w in polar form. (ii) find all the roots of 25 = √3-i in polar form. Show all the roots on an Argand diagram. (b) Use de Moivre's theorem to show that cos 50 = 16 cos 0 - 20 cos³0+5 cos 0. Hence, solve 32r5 - 40x³ + 10x = √3.
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