Simplify $\frac { 2 + i } { 5 + 2 i }$ and write the answer in standard form.
A) $- \frac { 12 } { 29 } + \frac { 1 } { 29 } i$
B) $\frac { 12 } { 29 } - \frac { 1 } { 29 } i$
C) $\frac { 12 } { 29 } + \frac { 1 } { 29 } i$
D) $\frac { 1 } { 29 } + \frac { 12 } { 29 } i$
E) $\frac { 1 } { 29 } - \frac { 12 } { 29 } i$

Question

Quizplus · Accepted Answer

To simplify the fraction, multiply both the numerator and denominator by the conjugate of the denominator, which is $5-2i$.
\begin{align*}
\frac{2+i}{5+2i} &= \frac{(2+i)(5-2i)}{(5+2i)(5-2i)} \
&= \frac{8+9i}{29} \
&= \frac{8}{29} + \frac{9}{29}i.
\end{align*}
Therefore, the answer is in standard form: $\frac{8}{29} + \frac{9}{29}i$, which is equivalent to $\boxed{	extbf{(C)}}$.

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Simplify $\frac { 2 + i } { 5 + 2 i }$