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.