Do the operation and express the answer in $a + b i$ form.
$$\frac { 4 + i } { 4 - i \sqrt { 3 } }$$
A) $\quad \frac { 16 - \sqrt { 3 } } { 19 } + \frac { 4 + 4 \sqrt { 3 } } { 19 } i$
B) $\quad \frac { 16 + \sqrt { 3 } } { 19 } + \frac { 4 - 4 \sqrt { 3 } } { 1 } i$
C) $\quad \frac { 19 + \sqrt { 3 } } { 19 } - \frac { 4 + 4 \sqrt { 3 } } { 19 } i$
D) $\quad \frac { 16 - \sqrt { 3 } } { 19 } - \frac { 4 - 4 \sqrt { 3 } } { 17 } i$
E)$$\frac { 19 - \sqrt { 3 } } { 19 } - \frac { 4 - 4 \sqrt { 3 } } { 19 } i$$

Question

Quizplus · Accepted Answer

To solve $\frac { 4 + i } { 4 - i \sqrt { 3 } }$, multiply the numerator and denominator by the conjugate of the denominator, $4 + i\sqrt{3}$, to get rid of the imaginary part in the denominator. Simplify the expression to get it in $a + bi$ form, which results in choice A.

Do the Operation and Express the Answer In a+bia + b ia+bi

Do the Operation and Express the Answer In $a + b i$