(a) 0 < r < 1
(b) z^6 - z^5 - z + 1 = 0
(c) z^2 - rz + 1 = 0

Find the value of r.

 z^6 - z^5 - z + 1 = 0

   ==> (z - 1)(z^5 - 1) = 0

   ==> z = 1 or z^5 = 1.

   ==> z = cos(72k) + i sin(72k)
           for k = 0, +-1, or +-2

 z^2 - rz + 1 = 0

   ==> r = z + 1/z = z + conjugate(z) 

         = 2 Real(z) = 2 cos(72k)

 0 < r < 1 

   ==> r = 2 cos(72) ~= 0.618034