The disc in question is {z: |z|<(n+1/2)pi}. I can't figure out how to apply Rouche to this. Any help would be appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

(This is in the context of showing all roots of zsin(z)=1 are real. I counted the zeros of zsin(z)-1 on the real axis and got 2n+2, and now I hope to get the same answer via the disc...)

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# How would I count the zeros of zsin(z)-1 in a complex disc?

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