🚀 go-pugleaf

HOW  TO  BRACKET  COMPLEX  ZEROS -  AN  EXAMPLE

The function considered is:

            F(Z)  =  Z^2+Z+1                                              
     (1)

The plots of the real and the imaginary part of (1) are obtained 
using MATLAB program

[x,y]=meshdom(-1:.05:1,0:.05:1);
colormap([1 1 1]);
z=sqrt((x.^2-y.^2+x+1).^2+((2*x+1).*y).^2).*cos(atan((2*x+1).*y./(x.^2-y.^
2+x+1)));
surf(x,y,z)

for the real part (figure 1) and

[x,y]=meshdom(-1:.05:1,0:.05:1);
colormap([1 1 1]);
z=sqrt((x.^2-y.^2+x+1).^2+((2*x+1).*y).^2).*sin(atan((2*x+1).*y./(x.^2-y.^
2+x+1)));
surf(x,y,z)

for the imaginary (figure 2). Subtracting the two and  using the MATLAB
contour command

x = -1:.01:0;
y = 0:.01:1;
[X,Y]=meshgrid(x,y);
colormap([1 1 1]);
Z=sqrt((X.^2-Y.^2+X+1).^2+((2*X+1).*Y).^2).*sin(atan((2*X+1).*Y./(X.^2-Y.^
2+X+1)))
-sqrt((X.^2-Y.^2+X+1).^2+((2*X+1).*Y).^2).*cos(atan((2*X+1).*Y./(X.^2-Y.^2
+X+1)));
%contour3(X,Y,Z,30)
contour(x,y,Z)

we obtain the figure 3. The figure 3 clearly indicates the positions of 
complex zeros.