Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Can you help me with this?

For $\lambda \in \mathbb{C}$, show that there exist $m,n \in \mathbb{Z}$ large enough (depending in $\lambda$) such that the equation $e^z = z+\lambda$ has exactly $m+n$ solution in $\{z\mid -2m \pi < \Im(z) < 2n \pi\}$ (where $\Im(z)$ is the imaginary part of $z$).

Thanks a lot! Jon

The idea is to use to use the Argument Theorem and to see what is the change of the arg.

share|improve this question
    
I fixed the math display and the definition of the set to the one which I think you mean (your notation was unclear). Please look it over to see if I correctly interpreted your question. –  Willie Wong Jan 18 '11 at 14:07

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.