I want to know about plotting complex function
显示 更早的评论
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
6 个评论
Jae Yoon Kim
2018-9-29
Walter Roberson
2018-9-29
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
2018-10-3
The coordinate transformation isn't very clear from your question. Can you define u and v ?
Walter Roberson
2018-10-3
So you compute f(z) and then say that u = real(f(z)) and v = imag(f(z))
Jan
2018-10-6
@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.
采纳的回答
Dimitris Kalogiros
2018-10-4
编辑：Dimitris Kalogiros
2018-10-5
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:
4 个评论
Jae Yoon Kim
2018-10-5
Walter Roberson
2018-10-5
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
2018-10-5
Put it where-ever you wanted z0 = 0+i0 ?
Dimitris Kalogiros
2018-10-5
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 )
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