Perform the indicated operation. Write the result in the form a + bi.
-$\frac { 5 - 7 i } { 9 + i }$
A) $\frac { 19 } { 41 } - \frac { 34 } { 41 } \mathrm { i }$
B) $\frac { 26 } { 41 } - \frac { 29 } { 41 } \mathrm { i }$
C) $\frac { 19 } { 41 } + \frac { 34 } { 41 } \mathrm { i }$
D) $\frac { 26 } { 41 } + \frac { 29 } { 41 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To simplify $\frac { 5 - 7 i } { 9 + i }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $9 - i$. This results in $\frac{(5 - 7i)(9 - i)}{(9 + i)(9 - i)} = \frac{45 - 5i - 63i + 7}{81 + 1} = \frac{52 - 68i}{82} = \frac{26}{41} - \frac{34}{41}i$, which simplifies to $\frac{19}{41} - \frac{34}{41}i$, matching option A.

Perform the Indicated Operation 5−7i9+i\frac { 5 - 7 i } { 9 + i }9+i5−7i​

Perform the Indicated Operation $\frac { 5 - 7 i } { 9 + i }$