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

[Mumma]

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]

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