Find the quotient. Write the answer in standard form.
-$$\frac { 2 + 3 i } { 5 + 2 i }$$
A) $\frac { 16 } { 29 } + \frac { 11 } { 29 } \mathrm { i }$

B) $\frac { 16 } { 21 } - \frac { 11 } { 21 } \mathrm { i }$

C) $\frac { 4 } { 21 } - \frac { 11 } { 21 } \mathrm { i }$

D) $\frac { 4 } { 29 } - \frac { 19 } { 29 } i$

Question

Find the quotient. Write the answer in standard form.
-$$\frac { 2 + 3 i } { 5 + 2 i }$$
A) $\frac { 16 } { 29 } + \frac { 11 } { 29 } \mathrm { i }$

B) $\frac { 16 } { 21 } - \frac { 11 } { 21 } \mathrm { i }$

C) $\frac { 4 } { 21 } - \frac { 11 } { 21 } \mathrm { i }$

D) $\frac { 4 } { 29 } - \frac { 19 } { 29 } i$

Quizplus · Accepted Answer

To divide complex numbers, you multiply the numerator and denominator by the conjugate of the denominator. The conjugate of $5 + 2i$ is $5 - 2i$. So, $\frac{2 + 3i}{5 + 2i} \cdot \frac{5 - 2i}{5 - 2i} = \frac{10 - 4i + 15i - 6i^2}{25 - 4i^2}$. Simplifying, we get $\frac{10 + 11i + 6}{25 + 4}$ because $i^2 = -1$. This simplifies further to $\frac{16 + 11i}{29}$, which is $\frac{16}{29} + \frac{11}{29}i$.

Find the Quotient 2+3i5+2i\frac { 2 + 3 i } { 5 + 2 i }5+2i2+3i​

Find the Quotient $\frac { 2 + 3 i } { 5 + 2 i }$