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 david hilbert January 26th, 2013 10:12 PM

minimum of a function

Hello from Greece.

Is there anybody out there who can help on this topic

" determine the minimum of the function f(z) defined where $f(z)=\left| 1-\frac{z}{e^z-1}\right|$
with z a complex number such us $0\leq \left|z \right|\leq 2\pi$ "

 CaptainBlack January 27th, 2013 10:53 PM

Re: minimum of a function

Have you considered treating this as a constrained minimisation problem in two variables?

CB

 CaptainBlack January 27th, 2013 11:15 PM

Re: minimum of a function

You have to be carefull how you define the function when $|z|=0$ since $e^z-1$ is undefined there, but behaves like $z$.

Also just plotting this over the constrained region shows that the minimum occurs when $z=0$, and is zero (at least withthe removable singularity at z=0 removed!).

CB

 tahir.iman January 28th, 2013 02:33 AM

Re: minimum of a function

find the value of z for $z= e^z -1$
$| a + bi |= \sqrt{ a^2 + b^2} \geq 0$

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