Question 464084
As it stands, the statement is not true.

Let {{{ x<>z }}}. Then both x and z are the roots of the quadratic equation {{{x^2 - x + 1 = 0}}}, and both roots are complex.  Hence one root is the complex conjugate of the other, by theorem in algebra.  
Also from algebra, xz = 1.

==> z = 1/x.

==> {{{z + 1/x = 1/x + 1/x = 2/x <>1 }}}, since 2/x would be a (non-real) complex number.