02
f(z) = 1/z
This image represents the complex function f(z) = 1/z. The complex plane above is colored according to the complex values of the function f(z). The function has a singularity at the origin z=0. Here the value of the function is infinity. The absolute value of 1/z decreases with increasing distance from the origin and, Correspondingly, the colors representing the function values are getting darker.
The singularity at z=0 is a pole of first order. A pole of first order always appears as a white spot. On a small circle around the pole all colors appear just once. The next example will show a pole of third order.