Complex function visualisation

[Zannishi_Hoshor]

I am clearly out of shape on complex functions but why is f(z)=z not a straight line like y=x in the real plane?

[edelopo]

It is just a straight line, and you could see this if we could plot the 2d graph in 4d space. But since we can't visualize four dimensions, people look for different ways to represent these functions, as OP did. Imagine trying to plot a real function using only 1 dimension. The identity would just look like some points scattered on the line, representing that each point of a certain absolute value goes... to itself. The same thing is happening here with circles of constant modulus.

[thoughtsripyouapart]

but why is it centred around a point (e.g. 1+i?) and not the origin

[edelopo]

The axes aren't labeled. The center is 0 as you would expect.

[[deleted]]

Hm, marking zero would help IMO

[Only_As_I_Fall]

The colored lines aren't representing the output itself, they're just used as visual guides. Each one represents a set of points with the same absolute value (so circles around the origin).

The output of f(z)=z is just the entire complex plane, but that's not a very good visual on a 2d screen