Simplify $\frac { 4 + 3 i } { 5 + 2 i }$ and write the answer in standard form.

A) $- \frac { 26 } { 29 } + \frac { 7 } { 29 } i$

B) $\frac { 26 } { 29 } - \frac { 7 } { 29 } i$

C) $\frac { 26 } { 29 } + \frac { 7 } { 29 } i$

D) $\frac { 7 } { 29 } + \frac { 26 } { 29 } i$

E) $\frac { 7 } { 29 } - \frac { 26 } { 29 } i$

Question

Simplify $\frac { 4 + 3 i } { 5 + 2 i }$ and write the answer in standard form.

A) $- \frac { 26 } { 29 } + \frac { 7 } { 29 } i$

B) $\frac { 26 } { 29 } - \frac { 7 } { 29 } i$

C) $\frac { 26 } { 29 } + \frac { 7 } { 29 } i$

D) $\frac { 7 } { 29 } + \frac { 26 } { 29 } i$

E) $\frac { 7 } { 29 } - \frac { 26 } { 29 } i$

Quizplus · Accepted Answer

To simplify $\frac { 4 + 3 i } { 5 + 2 i }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $5 - 2i$. This results in $\frac{(4+3i)(5-2i)}{(5+2i)(5-2i)} = \frac{20 - 8i + 15i - 6i^2}{25 - 4i^2}$. Since $i^2 = -1$, this simplifies to $\frac{26 + 7i}{29}$, or $\frac{26}{29} + \frac{7}{29}i$ in standard form.

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Simplify $\frac { 4 + 3 i } { 5 + 2 i }$