Divide.
-$$( 4 + 2 i ) \div ( 6 + 7 i )$$
A) $- \frac { 10 } { 13 } - \frac { 16 } { 13 }$ i
B) $\frac { 38 } { 85 } - \frac { 16 } { 85 } \mathrm { i }$
C) $\frac { 2 } { 17 } - \frac { 8 } { 17 } \mathrm { i }$
D) $- \frac { 38 } { 13 } - \frac { 16 } { 13 } \mathrm { i }$

Question

Quizplus · Accepted Answer

We can use the complex conjugate of the denominator to simplify:
\begin{align*}
(4+2i)\div(6+7i) &= \frac{(4+2i)\cdot (6-7i)}{(6+7i)\cdot (6-7i)} \
&= \frac{8+34i}{85} \
&= \frac{38}{85}-\frac{16}{85}i
\end{align*} Therefore, the answer is $\boxed{	extbf{(B)}}$.

Divide - (4+2i)÷(6+7i)( 4 + 2 i ) \div ( 6 + 7 i )(4+2i)÷(6+7i)

Divide
- $( 4 + 2 i ) \div ( 6 + 7 i )$