Simplify $\frac { 4 + 3 i } { 5 + 6 i }$ and write the answer in standard form.
A) $- \frac { 38 } { 61 } - \frac { 9 } { 61 } i$
B) $\frac { 38 } { 61 } + \frac { 9 } { 61 } i$
C) $\frac { 38 } { 61 } - \frac { 9 } { 61 } i$
D) $- \frac { 9 } { 61 } + \frac { 38 } { 61 } i$
E) $- \frac { 9 } { 61 } - \frac { 38 } { 61 } i$

Question

Quizplus · Accepted Answer

To simplify $\frac { 4 + 3 i } { 5 + 6 i }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $5 - 6i$. This results in $\frac{(4+3i)(5-6i)}{(5+6i)(5-6i)}$, simplifying to $\frac{20 - 24i + 15i - 18i^2}{25 - 36i^2}$. Since $i^2 = -1$, this further simplifies to $\frac{38 - 9i}{61}$, which is in standard form as $\frac{38}{61} - \frac{9}{61}i$.

Simplify 4+3i5+6i\frac { 4 + 3 i } { 5 + 6 i }5+6i4+3i​

Simplify $\frac { 4 + 3 i } { 5 + 6 i }$