Divide.
-$\frac { 1 + 3 i } { 5 + 6 i }$
A) $\frac { 23 } { 61 } + \frac { 9 } { 61 } \mathrm { i }$
B) $- \frac { 13 } { 61 } - \frac { 21 } { 61 } \mathrm { i }$
C) $- \frac { 23 } { 11 } - \frac { 9 } { 11 } \mathrm { i }$
D) $\frac { 13 } { 11 } - \frac { 9 } { 11 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To divide complex numbers, you multiply the numerator and denominator by the conjugate of the denominator. The conjugate of $5 + 6i$ is $5 - 6i$. Multiplying both the numerator and denominator by this conjugate, we get: $\frac{(1+3i)(5-6i)}{(5+6i)(5-6i)} = \frac{5 - 6i + 15i - 18i^2}{25 - 36i^2} = \frac{23 + 9i}{61}$, which simplifies to $\frac{23}{61} + \frac{9}{61}i$.

Divide - 1+3i5+6i\frac { 1 + 3 i } { 5 + 6 i }5+6i1+3i​

Divide
- $\frac { 1 + 3 i } { 5 + 6 i }$