Simplify equation of single pole IIR transfer function
$$H(z)\cdot H(z^{-1})= \frac{K}{1-\alpha \cdot e^{-j \omega}} \cdot \frac{K}{1-\alpha \cdot e^{+j \omega}}$$

$$= \frac{K^2}{1-\alpha \cdot (e^{-j \omega}+e^{+j \omega})+ \alpha^2} = \frac{K^2}{1 + \alpha^2- 2 \cdot \alpha \cdot Re\{e^{j \omega}\}} = \frac{K^2}{1 + \alpha^2- 2 \cdot \alpha \cdot \cos( \omega)} $$