Visually Check Analyticity
An analytic function preserves angles where . This means that the curves corresponding to constant values of and will intersect at right angles, just as those for and do.
Use mesh shading to demonstrate that is analytic by seeing that the mesh lines for the real (black) and imaginary (white) parts intersect at right angles.
You can see the function is not analytic, since the intersections are not at right angles.