Simplify by rationalizing the denominator. Write your answer in a +bi form.
-$\frac { - 9 } { - 4 + 8 i }$
A) $- \frac { 3 } { 4 } + \frac { 3 } { 2 } \mathrm { i }$
B) $\frac { 9 } { 20 } - \frac { 9 } { 10 } \mathrm { i }$
C) $- \frac { 3 } { 4 } - \frac { 3 } { 2 } \mathrm { i }$
D) $\frac { 9 } { 20 } + \frac { 9 } { 10 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator. In this case, the conjugate is -4-8i. So, we have:
$$\frac{-9(-4-8i)}{(-4+8i)(-4-8i)}=\frac{36+72i}{80}=\frac{9}{20}+\frac{9}{10}i$$
Therefore, the answer is D, $\frac { 9 } { 20 } + \frac { 9 } { 10 } \mathrm { i }$.

Simplify by Rationalizing the Denominator −9−4+8i\frac { - 9 } { - 4 + 8 i }−4+8i−9​

Simplify by Rationalizing the Denominator $\frac { - 9 } { - 4 + 8 i }$