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 January 26th, 2013, 10:12 PM #1 Newbie   Joined: Jan 2013 Posts: 1 Thanks: 0 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 $0\leq \left|z \right|\leq 2\pi$ " Thanks in advance!
 January 27th, 2013, 10:53 PM #2 Senior Member   Joined: Jan 2012 From: Erewhon Posts: 245 Thanks: 112 Re: minimum of a function Have you considered treating this as a constrained minimisation problem in two variables? CB
 January 27th, 2013, 11:15 PM #3 Senior Member   Joined: Jan 2012 From: Erewhon Posts: 245 Thanks: 112 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
 January 28th, 2013, 02:33 AM #4 Senior Member   Joined: Dec 2012 Posts: 148 Thanks: 0 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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