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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 cos5 - 20 cos³ 0+5 cos 0. Hence, solve 32r³-402³ + 10x = √√3.

(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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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