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I have the following question:

  1. Prove that the set $\{\exp(b_{n}z):n\in\mathbb N\}$ is linearly independent for some complex point $z\in\mathbb Z$.

  2. Prove that the set $\{\exp(b_{n}z):n\in\mathbb N\}$ is linearly independent for all $z\in\mathbb Z$.

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    What is $b_n$ (a priori we might have $b_n=0$ for all $n$)? Do you really talk about a set of *numbers* $e^{b_n z}$ for fixed $z$, or do you rather mean the set of fucntions $z\mapsto e^{b_n z}$?2012-09-05
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    @Zeraoulia I edited your post to make it a little clearer. Please look it over to make sure I didn't make any mistakes.2012-09-05
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    It would *still* be helpful to know about which vector space over which field we are talking (and what we know about $b_n$)2012-09-05

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