Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$\frac { \sqrt { 2 } + 8 i } { 3 - 4 i }$
A) $\frac { - 32 + 3 \sqrt { 2 } } { 25 } - \frac { 24 + 4 \sqrt { 2 } } { 25 }$ i
B) $\frac { - 32 + 3 \sqrt { 2 } } { 25 }$
C) $\frac { - 32 + 3 \sqrt { 2 } } { 25 } + \frac { 24 + 4 \sqrt { 2 } } { 25 }$ i
D) $\frac { 24 + 4 \sqrt { 2 } } { 25 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To simplify $\frac { \sqrt { 2 } + 8 i } { 3 - 4 i }$, we multiply both the numerator and the denominator by the conjugate of the denominator, which is $3 + 4i$. This results in $\frac { (\sqrt { 2 } + 8 i) (3 + 4 i) } { (3 - 4 i)(3 + 4 i) }$. Simplifying the numerator and denominator separately, we get $\frac { 3\sqrt { 2 } - 32 + (24 + 4\sqrt { 2 })i } { 25 }$, which simplifies to $\frac { - 32 + 3 \sqrt { 2 } } { 25 } + \frac { 24 + 4 \sqrt { 2 } } { 25 }$ i, matching choice C.

Simplify Write Your Answers in the Form of A+bi, Where 2+8i3−4i\frac { \sqrt { 2 } + 8 i } { 3 - 4 i }3−4i2​+8i​

Simplify Write Your Answers in the Form of A+bi, Where $\frac { \sqrt { 2 } + 8 i } { 3 - 4 i }$