Divide and express the result in standard form.
-$\frac { 5 } { 5 + i }$
A) $\frac { 25 } { 24 } - \frac { 5 } { 24 } \mathrm { i }$
B) $\frac { 25 } { 26 } - \frac { 5 } { 26 } \mathrm { i }$
C) $\frac { 25 } { 26 } + \frac { 5 } { 26 } \mathrm { i }$
D) $\frac { 25 } { 24 } + \frac { 5 } { 24 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To divide complex numbers, you multiply the numerator and denominator by the conjugate of the denominator. The conjugate of $5 + i$ is $5 - i$. Thus, $\frac { 5 } { 5 + i } \times \frac { 5 - i } { 5 - i } = \frac { 25 - 5i } { 25 + 1 } = \frac { 25 - 5i } { 26 }$, which simplifies to $\frac { 25 } { 26 } - \frac { 5 } { 26 } \mathrm { i }$.

Divide and Express the Result in Standard Form 55+i\frac { 5 } { 5 + i }5+i5​

Divide and Express the Result in Standard Form $\frac { 5 } { 5 + i }$