% p23: 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;
gamma = z.*sqrt(1+1./z.^2);
subplot(2,2,1)
surf(x,y,imag(gamma)); shading flat
xlabel('Re z'); ylabel('Im z'); zlabel('Im \gamma(z)')
gamma = sqrt(z.^2+1);
subplot(2,2,2)
surf(x,y,imag(gamma)); shading flat
xlabel('Re z'); ylabel('Im z'); zlabel('Im \gamma(z)')
gamma = sqrt(z+i).*sqrt(z-i);
subplot(2,2,3)
surf(x,y,imag(gamma)); shading flat
xlabel('Re z'); ylabel('Im z'); zlabel('Im \gamma(z)')
gamma = sqrt(z+i).*sqrt(z).*sqrt(-i./z+1);
subplot(2,2,4)
surf(x,y,imag(gamma)); shading flat
xlabel('Re z'); ylabel('Im z'); zlabel('Im \gamma(z)')
