Find the solution of $\displaystyle e^z = z\text{ in }|z|<2$

and $\displaystyle \tan x = x\text{ in }-\frac{3}{2}\pi<x<\frac{3}{2}\pi$

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- Mar 19th 2010, 03:31 PMGOKILLunusual equality
Find the solution of $\displaystyle e^z = z\text{ in }|z|<2$

and $\displaystyle \tan x = x\text{ in }-\frac{3}{2}\pi<x<\frac{3}{2}\pi$ - Mar 19th 2010, 04:54 PMdrumist
Neither of those can be solved analytically. You will need a numerical method, such as graphing on a calculator.

For example, on the first one, you could set $\displaystyle y=e^x-x$ and then find all the zeros graphically on $\displaystyle -2<x<2$. - Mar 19th 2010, 08:05 PMproscientia
I believe the first one is supposed to be a problem in complex analysis (use of $\displaystyle z$ rather than $\displaystyle x.)$ Perhaps Rouché’s theorem might help.

- Mar 24th 2010, 07:12 PMGOKILL
What is Rouche's theorem????

I have tried to solve this but it got fail >_<