Show how to calculate magnitude squared in a dsp system.?

Question

Analytically show that the magnitude squared frequency response equals unity at all frequencies. i.e |h(w)|^2 = 1
The transfer function of a digital filter, running at a sample rate fs = 10Khz is given by

H(z) = a + z ^ -1 / 1 +a . z ^ -1

Where z = e ^ jwt
and
|h (w)| ^2 = h (w) . h*(w) = h(w). h(-w)

Starting with
(a + e ^ (-jwt) ) / ( 1 + a . e^ (-jwt))

Answer 1

|(a + e ^ (-jωt) ) / ( 1 + a . e^ (-jωt))| =
(a + |e ^ (-jωt)| ) / ( 1 + a . |e^ (-jωt)|) =
(a + 1) / (1 + a) = 1 for all ω