Re: Can we define f(z)=sqrt(z*sin(z)) as analytic function?


Robert Israel wrote:
In article <1155665384.969566.262430@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Juryu <jufreire@xxxxxxxxx> wrote:
Thank you. I see what you mean. It makes sense, but, how do you explain
the fact that

f'(z) = [z*cos(z) + sin(z)] / [2*sqrt(z*sin(z))]

is positive for real z>0, negative for real z<0, (small z's, of
course), but is not zero at z=0?

You're using the wrong branch of sqrt when z < 0.

f(z) is an odd function.


I know I am doing something wrong, but I can't understand. Example: z_1
= -0.1, z_2 = 0.1
Then z_1 * sin(z_1) = z_2*sin(z_2) which is a positive number. why
should I use a different branch for z_1 and z_2 if it comes to the same
number?

.

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