On pages 3~4 of the chapter on Recirculating Delay Networks, Miller talks about using 'the multiplicative property of magnitudes to conclude that the magnitude of a complex reciprocal is the reciprocal of a real magnitude'.

Can anyone explain to me why the gain |H| is equal to 1 / |1 - gZ(-d)| ?

ie. why does a feedback gain of 0.8 result in a maximum output gain of 5? this would mean that if you had a feedback gain of 0.999 say, you'd get a max output gain of 1000 - is that really so??

I think I understand the concept behind this, but just not the maths.