1. The problem statement, all variables and given/known data

The conjugation property is expressed as $\displaystyle x^*[n] \stackrel{Z}{\leftrightarrow} X^*(z^*)$.

This property follows in a straightforward maner from the definition of the $\displaystyle z$-transform, the details of which are left as an exercise.

2. Relevant equations

Z-transform definition: $\displaystyle X(z)=\sum_{n=-\infty}^\infty x[n]z^{-n}$

3. The attempt at a solution

Given a complex sequence, its z-transform is

$\displaystyle Z\{x[n]\} = \sum_{n=-\infty}^\infty (x_R[n] + jx_I[n]) z^{-n} = X_R(z) + jX_I(z) = X(z)$

Hence, the z-transform of a conjugated sequence

$\displaystyle Z\{x^*[n]\} = \sum_{n=-\infty}^\infty (x_R[n] - jx_I[n]) z^{-n} = X_R(z) - jX_I(z) = X^*(z)$

Now, how come I didn't get the $\displaystyle z^*$, as in $\displaystyle X^*(z^*)$?

PS. I apologize beforehand for copying verbatim from physicsforums.