Divide.
-$$( 6 - 9 i ) \div ( 5 + 2 i )$$
A) $\frac { 4 } { 7 } + \frac { 19 } { 7 } \mathrm { i }$
B) $\frac { 16 } { 7 } + \frac { 19 } { 7 } \mathrm { i }$
C) $\frac { 48 } { 29 } + \frac { 33 } { 29 } \mathrm { i }$
D) $\frac { 12 } { 29 } - \frac { 57 } { 29 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To divide complex numbers, we must rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator. \begin{align*}
\frac{6-9i}{5+2i}&=\frac{(6-9i)(5-2i)}{(5+2i)(5-2i)} \
&=\frac{48-57i}{29} \
&=\boxed{\frac{12}{29}-\frac{57}{29}i}.
\end{align*} Therefore, the answer is choice $	extbf{(D)}.$

Divide - (6−9i)÷(5+2i)( 6 - 9 i ) \div ( 5 + 2 i )(6−9i)÷(5+2i)

Divide
- $( 6 - 9 i ) \div ( 5 + 2 i )$