- #1

nateHI

- 146

- 4

## Homework Statement

[itex]z=x+iy;

f(z)=sin(z)/z[/itex]

find f'(z) and the maximal region in which f(z) is analytic.

## Homework Equations

The sinc function is analytic everywhere.

## The Attempt at a Solution

Writing f(z) as [itex](z^{-1})sin(z)[/itex] and differentiating with respect to z using the chain rule I get...

[itex](-z^{-2})sin(z)+cos(z)/z[/itex]

However, this seems to simple since the context of the chapter of the book this problem comes from is cauchy-riemann. I would suspect I need to put f(z) in the form Re{f(z)}=u(x,y) and Im{f(z)}=v(x,y). Then [itex]df/dz[/itex] would be [itex]du/dx+idv/dx[/itex]. If that is the case then I'm in trouble because the I can't separate the imaginary part from the real part of [itex]sinc(z)[/itex].