Nyquist Plot vs. Complex Function Plot

[Bullington]

This is not a homework problem, I just am confused a little about the differences between a Nyquist plot and the plot of a complex function. I believe they are the same given the domain of the plot of a complex function is for all real numbers equal to or greater than zero. However, I am having a hard time demonstrating this. So what is the difference? Is there a difference?

My original goal was to get a geometric understanding of complex functions and seeing the difference between differential complex functions and non-differential complex functions. What programs can I use to get a geometric understanding of complex functions.

I'm using matlab, but I am open to any suggestions. My code is below and I'm trying to plot the transfer function 50/(s+3) with a nyquist function, and a scatter plot. I expected that the scatter plot was going to make the same shape as the nyquist function, but it doesn't. Any suggestions?

y=-10:0.001:10;
x=0:0.001:20;
z=x'*ones(1,length(y))+ones(1,length(x))'*1i*y;
fz=50*(z+3)\ones(length(z));
scatter(real(fz(:)),imag(fz(:)))
figure
nyquist(zpk([],[-3],50))

Thanks for checking this out!

 

[FactChecker]

I'm afraid that using Nyquist plots to understand functions of a complex variables is taking a wrong turn. Nyquist plots are used to analyse the stability of systems as a parameter changes. Complex valued functions of a complex variable are much more general and a very different subject. I recommend that you look at an introductory book on complex analysis. I can't recommend any shortcuts.

PS. If your goal is to understand system dynamics, you may be better off with an introductory book on stability and control.