Write the following expression as a complex number in standard form. $\frac { - 4 - 7 i } { - 5 - 8 i }$
A) $1 + i$
B) $\frac { 76 } { 89 } + \frac { 3 } { 89 } i$
C) $\frac { 32 } { 89 } + \frac { 35 } { 89 } i$
D) $\frac { 36 } { 89 } - \frac { 67 } { 89 } i$
E) $- \frac { 32 } { 39 } - \frac { 35 } { 39 } i$

Question

Quizplus · Accepted Answer

To simplify the given expression $\frac{-4 - 7i}{-5 - 8i}$, we multiply both the numerator and the denominator by the conjugate of the denominator, which is $-5 + 8i$. This results in $\frac{(-4 - 7i)(-5 + 8i)}{(-5 - 8i)(-5 + 8i)}$. Simplifying this expression gives $\frac{20 + 32i + 35i + 56}{25 + 64}$, which simplifies further to $\frac{76 + 67i}{89}$. Therefore, the expression in standard form is $\frac{76}{89} + \frac{67}{89}i$, which matches choice B.

Write the Following Expression as a Complex Number in Standard −4−7i−5−8i\frac { - 4 - 7 i } { - 5 - 8 i }−5−8i−4−7i​

Write the Following Expression as a Complex Number in Standard $\frac { - 4 - 7 i } { - 5 - 8 i }$