Visually Identify Features
You can identify multiple features in a complex function from its plot.
Looking at the plot of 
, you can easily see the zeros at the third roots of unity and the four poles at 
.
From the plot of 
, you can note that there are zeros of order two at 
and poles of order three at 
when 
is a non-positive integer.
The plot of 
shows more complicated behavior. You can see that there are no zeros, but there is a pole of order 3 at 
. There are also four poles of order one along each angle 
and 
. There are also poles of order one along the angles 0 and 
that accumulate at essential singularities at 
and 
.
