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

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) $\frac { 1 } { 29 } - \frac { 12 } { 29 } i$

Quizplus · Accepted Answer

To simplify the fraction, we need to multiply both the numerator and denominator by the complex conjugate of the denominator, which is $5-2i$. This gives us: $$\frac{2+i}{5+2i} = \frac{(2+i)(5-2i)}{(5+2i)(5-2i)} = \frac{8+9i}{29} = \frac{8}{29} + \frac{9}{29}i$$ Therefore, the answer is in standard form, and the best choice is $\boxed{	extbf{(C)}}$.

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