MATLAB: I want to know about plotting complex function

complex functioncomplex numbersplot

I want to know about this homework as i show you this images.
I should submit this homework including code,x-y plane graph and u,v plane graph.
z=x+iy and f(z)=2/(z-1)=u(x,y)+iv(x,y) (i is imaginary numbers)
please help me

Best Answer

clear; clc;
% entire z-plane
x=-3:0.01:3;
y=-3:0.01:3 ;
% our z region
zregion=[];
for n=1:length(x)
    for k=1:length(y)
        z=x(n)+y(k)*1i;
        if abs(z-2)<1
            zregion=[zregion z];
        end
    end
end
% mapping 
fzRegion=[];
for n=1:length(zregion)
    z=zregion(n);
    fz=2/(z-1);
    fzRegion=[fzRegion fz];
end
% plot these two regions
figure;
subplot(1,2,1);
plot(real(zregion), imag(zregion), 'b.'); zoom on; grid on; hold on; 
plot( [-5 5],[0 0 ], '-k', 'LineWidth', 2  );
plot( [0 0],[-5 5 ], '-k', 'LineWidth', 2  );
axis square; 
xlabel('x'); ylabel('y'); title('abs(z-2)<1')
subplot(1,2,2);
plot(real(fzRegion), imag(fzRegion), 'r.'); zoom on; grid on; hold on; 
plot( [-200 200],[0 0 ], '-k', 'LineWidth', 2  );
plot( [0 0],[-200 200 ], '-k', 'LineWidth', 2  );
axis square; 
xlabel('u'); ylabel('v'); title('f(z)');
But be careful... Point z1=1+j0 is a boundary point of your z-region. As z is approaching z1, f(z) going to infinity.
If you run the above script, you will receive the following graph:
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