What the difference between plotting the function f(z) (where its coefficients change with time) and plot of its zeros which evolves with time t

I use this function which has coefficints change with time t

first I plotted its roots (which evolve with time t) an I have got pathes in complex plane.

second I want to plot this function f(z),(which in complex variable zand its cofficients evolve with time t ) is the graph of this function pathes or serface? and if it is serface how can I plot it in complex plane?

for example if Iwant to plot this function'

\begin{align*}

f_(z) =(0.5000 + 0.0000i)+( 0.5001 + 0.8661i) z+(-0.2500 + 0.4330i)z^2

\end{align*}\\

[Aisha Mohamed]

Hi Dear,

Thank you very much for your answer, could I have a comment in your answer please? I think, Your answer is correct when the coefficients of this function are constants, but as I said, this function has coefficients that change over time t, meaning that, both the coefficients and the variable z in this function will change simultaneously.. Does that mean the graph of this function will be a surface and not path???

I will appreciate any help

Answer 1

[Chandra]

Hi,

The value of z is a complex value, so provide x and y values in z accordingly and provide the variable to function

>>x = 1:10; %real part of z.
>>y = 11:20; %imaginary part of z
>>z = x+i*y; %complex value
>>f_ =(0.5000 + 0.0000i)+( 0.5001 + 0.8661i)*z+(-0.2500 + 0.4330i)*z.^2
>> plot(real(f_),imag(f_)); %plotting the graph

Refer to real and imag of matlab

[Chandra]

Hi,

The z complex plane has two or three coefficients, if it has 2 coefficients then plot it is path, if it has 3 coefficients then it is surface plot (use surf matlab function)

x can be considered as a function of t and y is function of t and combined into z function

>>t = 0:0.2:2;
>>x = sin(2*pi*10*t) % example function of x with respect to t
>>y = cos(2*pi*10*t) % example function of y with respect to t
>>z = x+iy  %here z can be considered as 2 coefficients plane.