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 $\frac { 2 + i } { 5 + 2 i }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $5 - 2i$. This gives $\frac{(2+i)(5-2i)}{(5+2i)(5-2i)}$. Simplifying the numerator: $2*5 + 2*(-2i) + i*5 + i*(-2i) = 10 - 4i + 5i + 2 = 12 + i$. Simplifying the denominator: $5^2 - (2i)^2 = 25 - (-4) = 29$. Thus, the simplified form is $\frac{12+i}{29}$, or $\frac{12}{29} + \frac{1}{29}i$.

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