+0  
 
0
268
1
avatar+606 

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 $d+f$.

 May 6, 2018
 #1
avatar+21827 
+1

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 $d+f$.

 

\(\begin{array}{|rcll|} \hline a+bi \\ c+di \\ e+fi \\ \hline a+c+e+(b+d+f)i &=& -i \quad & | \quad e=-a-c \\ a+c-a-c+(b+d+f)i &=& -i \\ (b+d+f)i &=& -i \quad & | \quad b = 1 \\ (1+d+f)i &=& -i \quad & | \quad :i \\ 1+d+f &=& -1 \\ \mathbf{d+f} &\mathbf{=}& \mathbf{-2} \\ \hline \end{array}\)

 

laugh

 May 7, 2018

26 Online Users

avatar