Plotting inequalities on the complex plane

Despite using Matlab for several years, I am little ashamed but I have no idea how to plot the set on the complex plane that satisfies where . Is there any way to visualize such inequalities graphically on the complex plane, using Matlab? Should I use fimplicit or fcontour? Something other? Thanks in advance.

Answer 1

[Torsten]

It's only left to decide whether it's inside or outside ...

z = @(x,y)x+1i*y;
f = @(x,y)abs(1+z(x,y)+z(x,y).^2) - 4;
fimplicit(f)

Answer 2

[Sulaymon Eshkabilov]

Is that what you are trying to attain:

% Grid size:
N = 100;  
% Defined grid in X and Y planes:
[X, Y] = meshgrid(linspace(-4, 4, N), linspace(-4, 4, N));
% Create a grid of complex numbers:
Z = X + 1i * Y;
% Compute the Inequality by the given condition:
C = abs(1 + 2 * Z + Z.^2) < 4;

% Plot the set that satisfies the given Inequality Condition C:
scatter(real(Z(C)), imag(Z(C)), 'b.')
xlabel('Re part')
ylabel('Imag part')
title('Complex Plane Set at |1 + 2z + z^2| < 4')
grid on