Answer to Question #231375 in Chemical Engineering for pavani

Question

1) Is the function f(z)={[Rez-lmz]²/|z|² ,z≠0 ;0 ,z=0 Continuous at z=0?

Answer 1

Converse of CR relations: $f = u + iv$ be defined on$Br(z_0)$ such that ux,uy,vx,vy exist on$Br(z_0)$ and are continuous at$\space z_0$ . If u and v satisfies CR equations then$f′(z_0)$ exist and$f’ = ux + iv$

hence the given function with the constant “z” is also continuous at the z=0