What are the solutions for $\sin(z) = z$ in complex plane? I know the answer on real axis. I also read in another answered question on this site that there are infinite solutions to this equation(though there are references to theorems, like Picard's that I am not familiar with). All I can think of is to write it as $$\sin(x+iy) =x+iy$$ or $$\sin(x)\cosh(y)+i \cos(x)\sinh(y) = x + i y$$ and equate the real and imaginary parts. But after that, I have no clue how to solve it.
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I saw that question already. It only talks about the proof for infinite solutions to exist. What are those infinite solutions is my question. Any formula or pattern or closed form for those infinite solutions? Why so quick to close this question? – Srini Oct 10 '21 at 21:33
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Try one of these inversion theorems. There are others and there is no known inverse of $\sin(x)-x$ in terms of known functions. – Тyma Gaidash Oct 10 '21 at 21:35