Write the expression in standard form.
-$\frac { i } { 5 + i }$
A) $\frac { 1 } { 26 } + \frac { 5 } { 26 } \mathrm { i }$
B) $\frac { 1 } { 26 } - \frac { 5 } { 26 } \mathrm { i }$
C) $\frac { 1 } { 26 }$
D) $\frac { 5 } { 26 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To write the expression $\frac { i } { 5 + i }$ in standard form, we multiply the numerator and the denominator by the conjugate of the denominator, which is $5 - i$. This gives us $\frac { i(5 - i) } { (5 + i)(5 - i) }$. Simplifying, we get $\frac { 5i - i^2 } { 25 - i^2 }$, and since $i^2 = -1$, this further simplifies to $\frac { 5i + 1 } { 26 }$, or $\frac { 1 } { 26 } + \frac { 5 } { 26 } \mathrm { i }$.

Write the Expression in Standard Form i5+i\frac { i } { 5 + i }5+ii​

Write the Expression in Standard Form $\frac { i } { 5 + i }$