Simplify by rationalizing the denominator. Write your answer in a +bi form.
-$\frac { 9 + 8 i } { 5 - 4 i }$
A) $\frac { 13 } { 9 }$
B) $\frac { 77 } { 41 } - \frac { 4 } { 41 } \mathrm { i }$
C) $\frac { 77 } { 9 } - \frac { 76 } { 9 } \mathrm { i }$
D) $\frac { 13 } { 41 } + \frac { 76 } { 41 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, which is $5+4i$. We get:

$$\frac{9+8i}{5-4i} \cdot \frac{5+4i}{5+4i} = \frac{(9+8i)(5+4i)}{41} = \frac{13}{41} + \frac{76}{41}i$$

Therefore, the answer is D.

Simplify by Rationalizing the Denominator 9+8i5−4i\frac { 9 + 8 i } { 5 - 4 i }5−4i9+8i​

Simplify by Rationalizing the Denominator $\frac { 9 + 8 i } { 5 - 4 i }$