Problem:
Find the second order expansion of the following function around 2:
$\sqrt{5} \sqrt{-x^2}$
Answer:
$\begin{cases}
 i \sqrt{5} (x+1)-i \sqrt{5} & 2 \Im(x)-\Im\left((x+1)^2\right)<0 \\
 i \sqrt{5}-i \sqrt{5} (x+1) & \text{True}
\end{cases}$
{'source': 'AMPS', 'file': 'amps/mathematica/calculus/series_expansion/340.txt'}