Divide and express the result in standard form.
-$\frac { 3 } { 8 + i }$
A) $\frac { 24 } { 65 } - \frac { 3 } { 65 } \mathrm { i }$
B) $\frac { 24 } { 65 } + \frac { 3 } { 65 } \mathrm { i }$
C) $\frac { 8 } { 21 } + \frac { 1 } { 21 } \mathrm { i }$
D) $\frac { 8 } { 21 } - \frac { 1 } { 21 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To divide complex numbers, you multiply the numerator and denominator by the conjugate of the denominator. The conjugate of $8 + i$ is $8 - i$. So, $\frac { 3 } { 8 + i }$ becomes $\frac { 3(8 - i) } { (8 + i)(8 - i) }$. Simplifying, we get $\frac { 24 - 3i } { 64 + 1 }$ or $\frac { 24 - 3i } { 65 }$, which is $\frac { 24 } { 65 } - \frac { 3 } { 65 } \mathrm { i }$.

Divide and Express the Result in Standard Form 38+i\frac { 3 } { 8 + i }8+i3​

Divide and Express the Result in Standard Form $\frac { 3 } { 8 + i }$