FIR Filter - Transfer Function I am dealing with the transfer function of an FIR filter:


  $$H(z) = (1-0.5z^{-1})(1-2z^{-1})$$


I am having trouble determining which type of Linear-phase FIR filter it is, Type 1-4. I believe it may be Type 2, but not certain. 

Also I need to determine the frequency response of the filter. Is it just as simple as replacing the $z^{-1}$ terms with $e^{-j\omega}$ in order to get the frequency response? If so this results in frequency response of 


  $$H(e^{j\omega})=e^{-j\omega}(-2.5 + 2\cos(\omega))$$


And I am not sure how to take the magnitude or phase of that frequency response, any help would be greatly appreciated.
HINTS:


Just multiply the terms to get $H(z)$ in the form $$H(z)=h[0]+h[1]z^{-1}+h[2]z^{-2}$$ If you know the four types then you should immediately see which type it is.
Your frequency response looks good. The term in parentheses is real-valued. Does it change sign? You can directly write down magnitude and phase from that representation (just watch out for a negative sign, and what that means for the phase).