# Let be a complex number. Then the set of all complex numbers z satisfying the equation  for some real number k, is :

$\\\omega -\bar{\omega }z=k(1-z)\\ \omega -k=z(\bar{\omega }-k)\\ z=\frac{\omega -k}{\bar{\omega }-k}\\ z=\frac{\omega -k}{\bar{\omega }-\bar{k}}$
z is of the form $\frac{C}{\bar{C}}$
Therefore $|z| = 1\ and\ z\neq 1$