I've been amusing myself all day with doing some complex plotting in Sage. The default color scheme has 0=black, infinity=white, and red=real. A lot of the time, this doesn't work too well, but if you plot f/abs(f) the color will just depend on the complex argument. For example, if f = (z^5+1)/(z^5-1) we get:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivV64b_KFnBsBIRWiB5BJdP0qMWI5Ljb8M7xHQp59tGbKJf_u8snUTFQOggVhu52zDZ8ECBqtIEf0mAWj8L5_GScnSEoxX8Pb3M7AMBIL_9iIwa-fNd99d-b3tfPnrrjaMQeR76OZIRmaJ/s400/z55.png)
Or a more baroque example, f = z*log(z)*exp((z^5+1)/(z^5-1)^(1/2)):
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgehX4EsPMF0ZHc8UhlEQzY8j2K-W0GV2HLZlvqEzLhszUPzyUl4ITObna5TQfZM-Urw63uHqrKvBB4RxRAObVJ2mgZnEWrH5JY1vO4u8EpoX1G5gDtycYdymHlA8k0Tmk6ZKQGsdWhcDAa/s400/zlogzz5B.png)
Sometimes the default coloring is helpful, for example when showing the essential singularity at 0 of exp(1/z):