Divide and express the result in standard form.
-$$\frac { 4 - 2 i } { 5 - 9 i }$$
A) $\frac { 19 } { 53 } + \frac { 13 } { 53 } \mathrm { i }$
B) $- \frac { 19 } { 56 } - \frac { 13 } { 56 } \mathrm { i }$
C) $\frac { 2 } { 53 } + \frac { 46 } { 53 } \mathrm { i }$
D) $- \frac { 1 } { 28 } - \frac { 13 } { 56 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To divide complex numbers, you multiply the numerator and denominator by the conjugate of the denominator. The conjugate of $5 - 9i$ is $5 + 9i$. Multiplying, we get $\frac{(4 - 2i)(5 + 9i)}{(5 - 9i)(5 + 9i)}$, which simplifies to $\frac{20 + 36i - 10i - 18}{25 + 81}$, resulting in $\frac{2 + 26i}{106}$, or $\frac{19}{53} + \frac{13}{53}i$.

Divide and Express the Result in Standard Form 4−2i5−9i\frac { 4 - 2 i } { 5 - 9 i }5−9i4−2i​

Divide and Express the Result in Standard Form $\frac { 4 - 2 i } { 5 - 9 i }$