+610 There are 3 complex numbers $a+bi$, $c+di$, and $e+fi$. If $b=1$, $e=-a-c$, and the sum of the numbers is $-i$, find $d+f$.
+26367 There are 3 complex numbers $a+bi$, $c+di$, and $e+fi$. If $b=1$, $e=-a-c$,
and the sum of the numbers is $-i$, find $d+f$.
\(\begin{array}{|rcll|} \hline a+bi \\ c+di \\ e+fi \\ \hline a+c+e+(b+d+f)i &=& -i \quad & | \quad e=-a-c \\ a+c-a-c+(b+d+f)i &=& -i \\ (b+d+f)i &=& -i \quad & | \quad b = 1 \\ (1+d+f)i &=& -i \quad & | \quad :i \\ 1+d+f &=& -1 \\ \mathbf{d+f} &\mathbf{=}& \mathbf{-2} \\ \hline \end{array}\)
