How can I find how many solutions following equation have?
$$z+\sin{z}=i$$
I can make substitution $z=it$ and get
$$t+\sinh{t}=1$$
which has one real solution $t\approx0.4900730685$ thus $z\approx0.4900730685i$.
However with Mathematica I found more solutions, some of them: $$z\approx4.440301668+2.209373901i$$ $$z\approx-4.007976440-2.344091437i$$
And if there is infinitely many roots, is it possible to write formula for other roots using only first root I found?