Let x(n) = z^n where z = A exp(jω).
If x(n) is formed by sampling the continuous signal
x(t) = exp(st)
at integer multiples of a period T, then we see that
z = exp(sT).
x(n) forms a spiral in the z-plane.
A < 1 : spiral in
A > 1 : spiral out
A = 1 : no spiral (circle)
ω < 0 : spiral clockwise
ω > 0 : spiral counter-clockwise
ω = 0 : no spiral (trace real axis)
Notice that a frequency of ω is indistinguishable
from that of ω+2π. The discrete-ness in the time
domain causes the frequency domain to be periodic.
This is known as aliasing.