The color encoded phases of 
(above) and 
(below),
are constrasted in the negative half of the complex plane.
In the upper half of the image, the poles of are
clearly visible at negative integer values of 
:
the phase changes by 
around each pole, showing
a full revolution of the color wheel. This pattern is analogous
to one that would be seen in fluid flow generated by a semi-infinite
line of vortices.
In the lower half of the image, the poles of
(corresponding to the poles of ) and the
zeros between them are clear. Phase changes around the zeros
are of opposite sign to those around the poles. The fluid
flow analogy in this case involves a line of vortices of
alternating sign of circulation, resulting in a near
cancellation of flow far from the real axis.
