how to plot compelex function

I want to add some information that make this question more clear

1- I use p=[(0.9-0.124i) (0.4243 + 0.0017i) (0.10 + 0.3i)]; and as t change time = 0:0.01:2*pi (polynomial in z inthe second degree) f(z) = (0.10 + 0.3i) + (0.4243 + 0.0017i)z + (0.9-0.124i)z^2

the coefficients of p will cange with time by using this relation | f(t)> =exp(i t H)|f(0)>,for some H (given) and |f(0)> are the coefficients of p at t=o, and at every time I have new coefficients | f(t)> and plot the function p.

2- the function f(1/z) at every time must use the complex conjugate of the coeffecients of p (multiply in some constants)which also change with time t by the same way that coefficients of p do(in this case f(1/z) is the function of 1/z in the third degree) f(1/z) = (0.10 − 0.3i)z^-1 + (0.2121 − 0.0008i)z^−2 + (0.9 + 0.001i)z^−3.

How can I plot the two function in this case?

When I am trying to plot f(z) and f(1/z) I got paths in complex plane (not serface). and I am not sure that plots are correct.

I will appreciate any help

[Torsten]

So f will depend on t and on z :

f(z,t) = exp(i*t*H) * p * [z.^2;z;1] 

?

And

g(z,t) = exp(i*t*H) * conj(p) * [z.^3;z.^2;z]

?

And how do you want to plot f(z,t) and g(1/z,t) ?

If the above form of the functions is true, f and g are functions from C x R -> C.

I don't understand how you want to plot them.