% p22: sqrt(z^2-1) branch cut; 04/02/2008 SGLS
x = -2:.01:2; y = x;
[x,y] = meshgrid(x,y); z = x + i*y;
beta = sqrt(z.^2-1);
subplot(2,2,1)
surf(x,y,real(beta)); shading flat
xlabel('Re z'); ylabel('Im z'); zlabel('Re \beta(z)')
subplot(2,2,2)
surf(x,y,imag(beta)); shading flat
xlabel('Re z'); ylabel('Im z'); zlabel('Im \beta(z)')
beta = sqrt(z-1).*sqrt(z+1);
subplot(2,2,3)
surf(x,y,real(beta)); shading flat
xlabel('Re z'); ylabel('Im z'); zlabel('Re \beta(z)')
subplot(2,2,4)
surf(x,y,imag(beta)); shading flat
xlabel('Re z'); ylabel('Im z'); zlabel('Im \beta(z)')
