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Complex plotting


Mathematica folks,

I am trying to plot the function:

E^(3 z)/(1 + E^z) where z ranges from z = R (>0) to z = R + 2 Pi I.

When z = R, the value of the function is E^(3 R)/(1 + E^R)

When z = R + Pi I, the value of the function is E^(3 R)/(-1 + E^R)

When z = R + 2 Pi I, the value of the function is E^(3 R)/(1 + E^R) again.

I am trying to show with a plot that the magnitude of the function achieves
its maximum at z = R + Pi I.

I have tried using ComplexMap, but perhaps don't know how to fully utilize
it.

Help would be appreciated.

Diana

-- 
=====================================================
"God made the integers, all else is the work of man."
L. Kronecker, Jahresber. DMV 2, S. 19.


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