Derive a simple expression purely real for the magnitude

Question

Question: Answer the following questions about the system whose z-transform system function is

H(z) = 1 + 0.8z^-1
         1 - 0.9z^-1

(a) Determine the poles and zeros of H(z).

(b) Determine the difference equation relating the input and output of this filter.

(c) Derive a simple expression (purely real) for the magnitude squared of the frequency response |H(e^{jω^})|2.

(d) Is this filter a lowpass filter or a highpass filter? Explain your answer in terms of the poles and zeros of H(z).