Write the expression in $a + b i$ form. $\frac { \sqrt { 3 } + \sqrt { 2 } i } { \sqrt { 3 } - \sqrt { 2 } i }$
A) $\frac { 6 } { 5 } + \frac { 2 } { 5 } i$
B) $\frac { 1 } { 5 } - 2 \frac { \sqrt { 6 } } { 5 } i$
C) $\frac { 5 } { 6 } + \frac { \sqrt { 6 } } { 5 } i$
D) $\frac { 1 } { 5 } + 2 \frac { \sqrt { 6 } } { 5 } i$
E) $\frac { 5 } { 6 } - \frac { \sqrt { 6 } } { 5 } i$

Question

Quizplus · Accepted Answer

Multiply the numerator and denominator by the conjugate of the denominator, $\sqrt{3} - \sqrt{2}i$:$$\frac{\sqrt{3} + \sqrt{2}i}{\sqrt{3} - \sqrt{2}i} \cdot \frac{\sqrt{3} + \sqrt{2}i}{\sqrt{3} + \sqrt{2}i} = \frac{(\sqrt{3} + \sqrt{2}i)^2}{(\sqrt{3})^2 - (\sqrt{2}i)^2}$$$$= \frac{(\sqrt{3})^2 + 2\sqrt{3}\sqrt{2}i + (\sqrt{2}i)^2}{3 - 2i^2}$$$$= \frac{3 + 2\sqrt{6}i + 2i^2}{3 - 2(-1)}$$$$= \frac{3 + 2\sqrt{6}i - 2}{5}$$$$= \frac{1 + 2\sqrt{6}i}{5}$$

Write the Expression In a+bia + b ia+bi Form 3+2i3−2i\frac { \sqrt { 3 } + \sqrt { 2 } i } { \sqrt { 3 } - \sqrt { 2 } i }3​−2​i3​+2​i​

Write the Expression In $a + b i$ Form $\frac { \sqrt { 3 } + \sqrt { 2 } i } { \sqrt { 3 } - \sqrt { 2 } i }$