I am having a similar problem. At the moment I think it is a setting that can be turned on in the graph by the user in the front end, but not by the developer of the graph in the back end.
For instance, I have plotted two expressions z = -1 + 5i, w = 3 - 4i, which desmos initially interprets as straight lines with i as the independent variable
But turning on complex mode manually via the spanner gives
which is perfect and exactly what I want.
So @desmos, is there any way in which complex mode can be enabled by default? Thank you!