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Can you please help me finding an exact description of the set:

$$ E_{R}=\{\cos{z} | z \in \mathbb{C}, |z|>R\} $$

For any $0.

My feeling is the $E_R = \mathbb{C}$, for any $R$, but I don't know how to show it, if it's true.

  • 1
    Do you know the answer for $e^z$? Do you know Picard theorem?2012-01-22
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    Now that you've mentioned it, yes, Picard theorem can show that it's the complex plane minus the origin. You should post it as an answer, so I can mark it as the accepted answer.2012-01-22
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    Note that $\cos$ assumes the value $w=0$!2012-01-22

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