Perform the indicated operation. Write the result in the form a + bi.
-$\frac { 3 } { 2 + 7 i }$
A) $\frac { 6 } { 53 } - \frac { 21 } { 53 } \mathrm { i }$
B) $- \frac { 2 } { 15 } + \frac { 7 } { 15 } \mathrm { i }$
C) $- \frac { 2 } { 15 } - \frac { 7 } { 15 } \mathrm { i }$
D) $\frac { 6 } { 53 } + \frac { 21 } { 53 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To simplify $\frac { 3 } { 2 + 7 i }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $2 - 7i$. This gives $\frac { 3(2 - 7i) } { (2 + 7i)(2 - 7i) }$. Simplifying, we get $\frac { 6 - 21i } { 4 + 49 }$, which simplifies further to $\frac { 6 } { 53 } - \frac { 21 } { 53 }i$.

Perform the Indicated Operation 32+7i\frac { 3 } { 2 + 7 i }2+7i3​

Perform the Indicated Operation $\frac { 3 } { 2 + 7 i }$