How can complex polynomials be represented? I know that real polynomials (polynomials with real coefficients) are sometimes graphed on a 3D complex space ($x=a, y=b, z=f(a+bi)$), but how are polynomials like $(1+2i)x^2+(3+4i)x+7$ represented?

Plotting $P(z) $ and $P:\mathbb{C}\rightarrow\mathbb{C}$, if you want to use a cartesian coordinate system give a 4D image because the input can be rappresented by the coordinate $(a,b)$ where $z=a+bi$, and the output too. 
So the points (coordinates) of the graph are of the kind 
$$(a,b,Re(P(a+bi)),Im(P(a+bi)))$$ 
and they belong to the set $\mathbb{R}^4$ (set of 4-uple of $\mathbb{R}$).
I think is impossible for evry human to watch a 4D plot on paper, but if you do a 3D plot with an animation, the timeline is your 4th dimension, and you can see how the 3d plot changes when the time (4th variable) changes.
I hope that is correct. At least this is how i represent in my mind 4D objects.
ps:I apologize in advance for any mistakes in my English, I hope that the translator did a good job :).
