graphing complex functions
hey math lads, non-mather here.
i'm doing a TOK title for my IB essay (not relevant but you can look that up) and i'm discussing complex functions.
my main argument is that mathematicians can't realistically graph complex functions because "a complex function maps a 2D input to a 2D output and properly graphing it would require 4D" (source: 10 second google search)
my first question is:
whether this is actually true, and if so, why a 2D input on a 2D output would require 4D.
and my second question is:
if so, why mathematicians would NEED to graph complex functions? mathematicians create various methods of graphing complex functions, however, if it doesn't 100% reflect (which i assume it doesn't) what value does it have to the mathematician? -> tl;dr: why do you need to graph complex functions even tho they can't be accurately graphed without 4D?
ty lads