Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$\frac { 5 + i } { - 1 - 7 i }$
A) $- \frac { 6 } { 25 } + \frac { 17 } { 25 } i$
B) $- \frac { 6 } { 25 }$
C) $- \frac { 6 } { 25 } - \frac { 17 } { 25 } \mathrm { i }$
D) $\frac { 17 } { 25 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To simplify $\frac { 5 + i } { - 1 - 7 i }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $-1 + 7i$. This results in $\frac{(5+i)(-1+7i)}{(-1-7i)(-1+7i)}$. Simplifying the numerator and denominator separately gives $\frac{-5-35i+i+7i^2}{1-49i^2}$, where $i^2 = -1$. This simplifies further to $\frac{-5-34i-7}{1+49}$, which simplifies to $\frac{-12-34i}{50}$, or $-\frac{6}{25} + \frac{17}{25}i$, matching choice A.

Simplify Write Your Answers in the Form of A+bi, Where 5+i−1−7i\frac { 5 + i } { - 1 - 7 i }−1−7i5+i​

Simplify Write Your Answers in the Form of A+bi, Where $\frac { 5 + i } { - 1 - 7 i }$