Question
Asked Dec 4, 2019
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Part ii only please!

If w is a complex root of z7 - 1 = 0.
.5
z
3
Show that w is a solution of 2 z
z
z
z 1 = 0.
i.
Find a quadratic equation with real coefficients having a root www
ii.
2т
Зп
1
TT
iii. Prove that cos
7
COS
7
COS
7
2
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If w is a complex root of z7 - 1 = 0. .5 z 3 Show that w is a solution of 2 z z z z 1 = 0. i. Find a quadratic equation with real coefficients having a root www ii. 2т Зп 1 TT iii. Prove that cos 7 COS 7 COS 7 2

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Expert Answer

Step 1

Refer to the we need to find the show the provided equations,

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7-1 0 Then to show (i)- 1 0 (ii)Find quacratic eqn for root o+ o + 2T - Cos 7 Зл - cos 7 1 (it)cos 7 2

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Step 2

To solve question 1 as,

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:'-1= 0 +:' +:+1)= 0 (:-1)(:* +. Use product rule (:-1) = 0 or :+ +:' + :' +: +1) = 0 (:' 6. +:+:+1= 0

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Step 3

Now to solve part2 ...

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we know,1+ @+m² = 0 @+ w² + @* = 0 -1+@w° =0 ) -1=0 -1+i3 also @= 2 -1±i3 0-1= -1 2 -3±i3

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