x(n) = z^n

z = + j
  = exp(j)

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Mathematical Notes

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.