% Modified from Prof. Womersley's geom.m
% MATH1251: File = geom2.m
% Plot regions in complex plane
format compact

w = -3 + 4i

r = 5

npts = 400;
t = (2*pi/npts)*[0:npts];
z = w + r*(cos(t)+i*sin(t));
x = real(z); y = imag(z);
xlim = [floor(min(x))-1 ceil(max(x))+1]
ylim = [floor(min(y))-1 ceil(max(y))+1]

figure(1)
subplot(3,2,1)
plot(z, 'b')
hold on
plot(w, 'b*');
hold off
grid on
title(['|z +3-4i| = ' num2str(r)]);
xlabel('Re(z)')
ylabel('Im(z)')
set(gca, 'XLim', xlim) 
set(gca, 'YLim', ylim)
axis square

subplot(3,2,2)
plot(z, 'b')
hold on
fill(x, y, 'c')
plot(w, 'b*');
hold off
grid on
title(['|z +3-4i| \leq ' num2str(r)]);
xlabel('Re(z)')
ylabel('Im(z)')
set(gca, 'XLim', xlim) 
set(gca, 'YLim', ylim)
axis square

subplot(3,2,3)
plot(z, 'b--')
hold on
fill([x xlim(2) xlim(1) xlim(1) xlim(2) xlim(2)], ...
     [y ylim(1) ylim(1) ylim(2) ylim(2) ylim(1)], 'c', 'EdgeColor', 'None')
plot(w, 'b*');
hold off
grid on
title(['|z - ' num2str(w) '| > ' num2str(r)]);
xlabel('Re(z)')
ylabel('Im(z)')
set(gca, 'XLim', xlim) 
set(gca, 'YLim', ylim)
axis square

subplot(3,2,4)
a = -4;
I = find(x>=a);
J = find(abs(x-a)<1e-1);
plot(z, 'b')
hold on
plot([a a], ylim, 'b');
fill(x(I), y(I), 'c')
plot(w, 'b*');
hold off
grid on
title(['|z - ' num2str(w) '| \leq ' num2str(r) ' and Re(z) \geq -4']);
xlabel('Re(z)')
ylabel('Im(z)')
set(gca, 'XLim', xlim) 
set(gca, 'YLim', ylim)
axis square

t1 = (pi/800)*[0:200];
z1 = w + r*(cos(t1)+i*sin(t1));
x1 = [real(w) real(z1)]; y1 = [imag(w) imag(z1)];

subplot(3,2,5)
plot(z, 'b')
hold on
fill(x1, y1, 'c')
plot(w, 'b*');
hold off
grid on
title(['|z +3 -4i| \leq ' num2str(r) ' and 0 \leq Arg(z+3-4i) \leq \pi/4']);
xlabel('Re(z)')
ylabel('Im(z)')
set(gca, 'XLim', xlim) 
set(gca, 'YLim', ylim)
axis square