Complex number question. z+1/z? (1 Viewer)

Mumma

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Attatched is the entire question, parts (a) to (c).
(a) and (b) I can do pretty easily, but (c) im not sure on how to proceed with.
 

littleboy

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using part b and divide both sides by z^3.
so it becomes :

z^3 + 1/Z^3 +1 = (z+1/z -2cos2pi/9)(z+1/z-2cos4pi/9)(z+1/z - cos8pi/9)
take out 8 from the right hand side and equate the real parts
 

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