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How do I solve $$\sin(z)=5$$ for all complex $z$?

I have tried using the definition of $\sin$ in terms of $\exp$ but I don't get far. I have tried setting $z=x+iy$ and considering trig identities but this didn't help either, neither did the Taylor series for $\sin$. thanks

Loli
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    Can you elaborate at all on how far you got with the exponentials definition of $\sin$? : ) Some working would perhaps help us to diagnose your problem better – Izaak van Dongen Jan 18 '20 at 21:57
  • @IzaakvanDongen Are you saying I should focus on the definition as that's the way to go? (sorry a bit frustrated i've spent a long time on this) – Loli Jan 18 '20 at 22:02
  • Yes, the exponentials definition is the right way to go. The initial hint is to rearrange and solve for $e^{iz}$. – Izaak van Dongen Jan 18 '20 at 22:03
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    @IzaakvanDongen lol now it looks too easy : ) i think not knowing how to tackle it was the main problem, thank you! – Loli Jan 18 '20 at 22:07
  • Compare https://math.stackexchange.com/q/1166562 –  Jan 19 '20 at 01:58

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