# Cauchy Riemann Equations (basic doubt)

 Math Emeritus Sci Advisor Thanks PF Gold P: 38,708 Let g(x, y)= 1 if xy is not 0, 0 if xy= 0 and let f(z)= g(x,y)(1+ i)= g(x, y)+ ig(x,y) where z= x+ iy. Then $$\frac{g(x,y)}{\partial x}= \frac{\partial g(x,y)}{\partial y}= 0$$ for (x,y)= (0, 0) so the Riemann-Cauchy equations are satisfied there but the function is not even continuous at (0, 0).