MATLAB: Mapping a filled circle ,like [(abs(z-1)<=1) by any mapping function

Question

How can I map a filled circle, like ( abs(z-1)) that z is the complex ?

Answer 1

A solution that help me and maybe useful for others (with mapping funcion -(z+1)/(z-1) and -i*cos(z/2))

clear all

clc

t=0:0.1:6.3;

y=sin(t);

x=cos(t)+1;

plot(x,y);

fill(x,y,'r');

z=complex(x,y);

u=-(z+1)/(z-1)

k=-i*cos(z/2)

s=real(u);

t=imag(u);

h=real(k);

g=imag(k);

subplot(2,2,1)

title('|z-1|<1')

hold all

fill(x,y,'r')

plot([-3,3],[0,0],'k');

plot([0,0],[-3,3],'k');

axis off equal

subplot(2,2,2)

title('f(z)=-(z+1)/(z-1) answer:-1.03+0.0003j')

hold all

scatter(s,t,20,'filled')

plot([-3,3],[0,0],'k');

plot([0,0],[-3,3],'k');

axis off equal

subplot(2,2,[3,4])

title('f(z)=-j*cos(z/2)')

hold all

fill(h,g,'g')

plot([-1,1],[0,0],'k');

plot([0,0],[-1.5,0.5],'k');

axis off equal