Poles of an exponential function

This is a bit embarrassing since I know I've done this problem before.

I was trying to respond to a post and this problem came up. Where are the poles in the expression $\displaystyle e^{-z^2}= cos(z^2) - i ~ sin(z^2)$? I know it's a simple problem but I just can't wrap my mind about it. (Headbang)

Thanks!

-Dan

Re: Poles of an exponential function

Quote:

Originally Posted by

**topsquark** Where are the poles in the expression $\displaystyle e^{-z^2}= cos(z^2) - i ~ sin(z^2)$? I know it's a simple problem but I just can't wrap my mind about it.

There are no poles, $\displaystyle f(z)=e^{-z^2}$ is holomorphic in $\displaystyle \mathbb{C}$. :)

Re: Poles of an exponential function

Quote:

Originally Posted by

**FernandoRevilla** There are no poles, $\displaystyle f(z)=e^{-z^2}$ is holomorphic in $\displaystyle \mathbb{C}$. :)

Thanks. That was my first thought but I managed to make things complicated. It drives my students nuts because I will do a derivation in 10 lines that can often be done in two. :)

-Dan