Every independent variable should be graphed perpendicular. X and Y when graphed are perpendicular. If they are not graphed perpendicular it indicates that a change in X position must change Y (or vice versa) whereas being perpendicular makes it clear that they are independent and you can change one without any thought that you're changing the value of the other.

Complex numbers have 2 independent variables. The real and the imaginary parts. You can change one part without being forced to change the other. So you graph them perpendicular.

It's not really a convention, it's a rule that each independent variable is perpendicular (or else they aren't independent!). Complex numbers have 2 independent variables.