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

Quizplus · Accepted Answer

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

Simplify 4+3i5+2i\frac { 4 + 3 i } { 5 + 2 i }5+2i4+3i​

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