A question regarding z transform and its magnitude response
The frequency response of a given filter is calculated evaluating $H(z)$ in the unit circle, i.e. $z=e^{j\omega}$.

Hint 1:

Note that you can express your transfer functions as follows:
$$H(e^{j\omega})=\frac{1-a^*e^{j\omega}}{e^{j\omega}-a}=\frac{1}{e^{j\omega}}\cdot\frac{1-a^*e^{j\omega}}{1-ae^{-j\omega}}$$

Hint 2:

There is a property that states that given any complex number $z$, the following equality holds:

$$|z|=|z^{*}|$$

Can you solve it now?