The formula for the rational function

                          
        (z+5)(z-6)(z-1-i)^4
r(z) = ------------------------- 
        (z-2-3i)^3 (z-3)(z+1-3i)

• The zero at 6 has order 1. Note that the colors cycle through red yellow green blue purple in counterclockwise order (like the standard plane).
• The zero at 1+i has order 4, since the colors cycle through 4 times as you pass counterclockwise around the zero.
• The pole at 2+3i has order 3 because the colors cycle 3 times in the opposite order.
• Near infinity, the colors cycle once in the same order as the standard plane, so that means that r(z) behaves like Cz, for some constant C, near infinity. Thus r(1/z) behaves like C/z for z near zero and hence r has a pole of order 1 at infinity.