Divide.
-$9 \div ( 4 \mathrm { i } )$
A) $- \frac { 4 } { 9 } \mathrm { i }$
B) $\frac { 9 } { 4 } \mathrm { i }$
C) $- \frac { 9 } { 4 } \mathrm { i }$
D) $\frac { 4 } { 9 } i$

Question

Quizplus · Accepted Answer

To divide by a complex number, we multiply the numerator and denominator by the complex conjugate of the denominator. In this case, the complex conjugate of $4i$ is $-4i$, so \begin{align*}
\frac{9}{4i} &= \frac{9}{4i} \cdot \frac{-4i}{-4i} \
&= \frac{-36i}{-16} \
&= \frac{9}{4}i.
\end{align*} Thus the answer is $\boxed{	ext{(C)}}.$

Divide - 9÷(4i)9 \div ( 4 \mathrm { i } )9÷(4i)

Divide
- $9 \div ( 4 \mathrm { i } )$