# If $f: U \rightarrow \mathbb{C}$ is entire, and satisfies $f(1/\sqrt{n})=1/n$, then what is the value of $f(-i)?$

This question is a homework question for my Complex analysis class, and is asked in context of the Identity Theorem (I do not need to show this):

If a holomorphic function defined on a connected open set $U$ is zero at every point of a sequence $\{z_j\}\subset U -􀀀 \{z_0\}$ converging to $z_0 \in U$ as $j$ goes to $1$, then $f$ is identically zero.

Am I not able to conclude that $f(z) = z^2$, and therefore $f(-i) = -1$? The reason I am questioning this is because of the context in which the problem was presented to me, as well as hints from my teacher that this is a "trick question".

Yes, $f(z)=z^2$. Since $f(1/\sqrt{n})=1/n=(1/\sqrt{n})^2$ for all $n$ and $\lim_{n\to \infty}1/\sqrt{n}=0$, by analytic continuation, we conclude that $f(z)=z^2$. So $f(-i)=-1$.