I want to know about plotting complex function

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

[Walter Roberson]

http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer

[Jae Yoon Kim]

sorry... I don't know anything about matlab. So I ask like this I'm very sorry for this.

[Walter Roberson]

http://www.mathworks.com/matlabcentral/answers/8026-best-way-s-to-master-matlab

We are not going to give you the answer. However, if you give a try and encounter an error that you are having trouble understanding, then you can post the code and a complete copy of the error message and we will try to explain why that code produces that message.

[Zenin Easa Panthakkalakath]

The coordinate transformation isn't very clear from your question. Can you define u and v ?

[Walter Roberson]

So you compute f(z) and then say that u = real(f(z)) and v = imag(f(z))

[Jan]

@Jae Yoon Kim: Please do not edit away a question after answers have been given. This is impolite and not respectful for the effort of the ones, who spent their time to help you. Thanks.

Answer 1

[Dimitris Kalogiros]

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:

[Jae Yoon Kim]

Thank you so much!! Can I ask you some question?? I want to z0 = 0+io How can I do this??

[Walter Roberson]

z0 = complex(0, 0);

That is the only way to get a variable whose real and imaginary parts are both 0. In nearly any other context, MATLAB will notice that the imaginary part is 0 and will automatically drop it, leaving you with a variable that is not specifically marked as imaginary.

The only time that z0 = 0; meaningfully differs from z0 = complex(0, 0); has to do with accessing external interfaces that might require a variable that is internally marked as being complex.

[Walter Roberson]

Put it where-ever you wanted z0 = 0+i0 ?

[Dimitris Kalogiros]

If you want to calculate f(zo), where zo=0+j0 , you have to do the followings:

zo=complex(0,0);
wo=2/(zo-1);  % wo=f(zo)

But be aware that zo=0+j0 does not belong to your area of interest ( |z-2|<1 )