Re: Help with analysis of complex function

From: Diana (diana53_at_earthlink.net)
Date: 11/19/04 

Date: 19 Nov 2004 08:56:34 -0800

Thanks Wade, I understand...

The World Wide Wade <waderameyxiii@comcast.remove13.net> wrote in message news:<waderameyxiii-731982.11094918112004@news.supernews.com>...
> In article <t53nd.2105$Tq6.946@newsread3.news.pas.earthlink.net>,
> "Diana" <diana53xiii@earthlink.remove13.net> wrote:
>
> > I am trying to show that the magnitude of the following function achieves
> > its maximum at z = R + Pi I.
> >
> > E^(3 z)/(1 + E^z) where z ranges from z = R (>0) to z = R + 2 Pi I.
>
> |e^(3z)/(1 + e^z)| = |e^(3z)|/|1 + e^z| = e^(3R)|/|1 + e^z|. You maximize
> the last expression by minimizing the denominator. But 1 + e^(R+it)
> describes a circle of radius e^R, centered at 1, as t goes from 0 to 2Pi.
> Where does that cirlce have minimum modulus?