Find an entire function $f$ such that $f(n+in)=0$ for every integer $n$ ($n$ can be positive, negative or zero). Give the most elementary example.
This is a problem from Conway at the end of the Weierstrass factorization theorem section. Can anyone help me construct this infinite product? I know that's where this is heading, but I cannot seem to see what I need to do for this, the book lacks an example like this.
Edit: To be clear here I'm looking for an infinite product likely derived using the Weierstrass factorization theorem. Out of context, the book's wording is weak but that is what they surely mean.