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**Z-transform of a conjugated sequence ("a straightforward" exercise)**

## Homework Statement

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

This property follows in a straightforward maner from the definition of the [itex]z[/itex]-transform, the details of which are left as an exercise.

## Homework Equations

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

## The Attempt at a Solution

Given a complex sequence, its z-transform is [tex]Z\{x[n]\} = \sum_{n=-\infty}^\infty (x_R[n] + jx_I[n]) z^{-n} = X_R(z) + jX_I(z) = X(z)[/tex]

Hence, the z-transform of a conjugated sequence [tex]Z\{x^*[n]\} = \sum_{n=-\infty}^\infty (x_R[n] - jx_I[n]) z^{-n} = X_R(z) - jX_I(z) = X^*(z)[/tex]

Now, how come I didn't get the [itex]z^*[/itex], as in [itex]X^*(z^*)[/itex]?

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