Perform the indicated operation. Write the result in the form a + bi.
-$\frac { 7 - 3 i } { 4 + 8 i }$
A) $\frac { 1 } { 20 } - \frac { 17 } { 20 } \mathrm { i }$
B) $\frac { 13 } { 5 } - \frac { 11 } { 5 } \mathrm { i }$
C) $- \frac { 1 } { 48 } + \frac { 17 } { 48 } \mathrm { i }$
D) $- \frac { 13 } { 12 } + \frac { 17 } { 48 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To simplify $\frac { 7 - 3 i } { 4 + 8 i }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $4 - 8i$. This gives $\frac{(7 - 3i)(4 - 8i)}{(4 + 8i)(4 - 8i)}$. Simplifying, we get $\frac{28 - 56i - 12i + 24}{16 + 64}$, which simplifies further to $\frac{52 - 68i}{80}$, or $\frac{13}{20} - \frac{17}{20}i$, which matches choice A.

Perform the Indicated Operation 7−3i4+8i\frac { 7 - 3 i } { 4 + 8 i }4+8i7−3i​

Perform the Indicated Operation $\frac { 7 - 3 i } { 4 + 8 i }$