Question 2
Let $k$ be a real number such that the system
$$
\begin{aligned}
|25 + 20i - z| &= 5 \\
|z - 4 - k| &= |z - 3i - k|
\end{aligned}
$$
has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i = \sqrt{-1}$.
$$
\begin{aligned}
|25 + 20i - z| &= 5 \\
|z - 4 - k| &= |z - 3i - k|
\end{aligned}
$$
has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i = \sqrt{-1}$.