Find the quotient. Write the answer in standard form.
-$$\frac { 4 + 3 i } { 5 + 3 i }$$
A) $\frac { 29 } { 34 } + \frac { 3 } { 34 } \mathrm { i }$
B) $\frac { 11 } { 34 } - \frac { 27 } { 34 } \mathrm { i }$
C) $\frac { 11 } { 16 } - \frac { 3 } { 16 } \mathrm { i }$
D) $\frac { 29 } { 16 } - \frac { 3 } { 16 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To divide complex numbers, you multiply the numerator and denominator by the conjugate of the denominator. The conjugate of $5 + 3i$ is $5 - 3i$. So, $\frac{4 + 3i}{5 + 3i} \cdot \frac{5 - 3i}{5 - 3i} = \frac{(4 + 3i)(5 - 3i)}{(5 + 3i)(5 - 3i)} = \frac{20 - 12i + 15i - 9}{25 + 9} = \frac{11 + 3i}{34}$, which simplifies to $\frac{11}{34} + \frac{3}{34}i$.

Find the Quotient 4+3i5+3i\frac { 4 + 3 i } { 5 + 3 i }5+3i4+3i​

Find the Quotient $\frac { 4 + 3 i } { 5 + 3 i }$