Question

Show that
x?y*(x + iy)
f(2)=
20
10
x + y
+y!
f(0) = 0
Z=0
is not analytic at the origin, althoug!
Cauchy-Riemann equations are satisfied
What is your opinion in this case?​

Answer 1

Answer:

We see that f (z) = z2 satisfies the Cauchy-Riemann conditions throughout the complex plane. Since the partial derivatives are clearly continuous, we conclude that f (z) = z2 is analytic, and is an entire function.