The problem
H(e^{j0.2\pi}) = {\frac{1 - 1.25e^{-j0.2\pi}}{1 - 0.8e^{-j0.2\pi}}}
Solves to H(e^{j0.2\pi}) = 1.25e^{j0.210\pi}
Attempts
I'm really not sure how to get that answer, but I've tried a number of different approaches
Multiplying by complex conjugate
Multiplying by...