6. Let $m, n$ be non-zero real numbers, $i$ be the imaginary unit, $z \in \mathbf{C}$, then the equations
$$
\begin{array}{l}
|z+n i|+|z-m i|=n \\
\text { and }|z+n i|-|z-m i|=-m
\end{array}
$$

in the same complex plane (with $F_{1}, F_{2}$ as foci) are ( ).

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Here is the translation, maintaining the original format and line breaks.
(B)
6. 【Analysis and Solution】From the problem,
(1) represents an ellipse with foci at $F_{1}(0,-n), F_{2}(0, m)$,
(2) represents one branch of a hyperbola with foci at $F_{1}(0,-n), F_{2}(0, m)$.

From (1), we know $n>0$, and $n=|z+n i|+|z-m i| \geqslant|n+m|$,
so $m<0$; then from (2) we get
$$
|z+n i|+|z-m i| \geqslant-m<n \text {. }
$$

Thus, the positions of $F_{1}, F_{2}$ can only be (B) or (D). From (3), we know that the points on the hyperbola are closer to $F_{2}$, so the situation is as shown in (B).