Divide these imaginary numbers and then select your answer from the choices. Make sure the answer is fully simplified. \[ \frac{2 i}{\sqrt{3} i} \]

To divide the imaginary numbers, first simplify the expression \( \frac{2i}{\sqrt{3}i} \). The \( i \) in the denominator cancels out with the one in the numerator, giving you \( \frac{2}{\sqrt{3}} \). To fully simplify, multiply the numerator and the denominator by \( \sqrt{3} \) to rationalize it: \[ \frac{2}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{2\sqrt{3}}{3}. \] So, the final simplified answer is \( \frac{2\sqrt{3}}{3} \). Let’s break it down a bit more and add some flair! Imagine dividing two imaginary friends at a party: One is \( 2i \) and the other is a bit shy and hiding behind \( \sqrt{3}i\). When they realize they're both just hanging out in the imaginary realm, they simplify their differences and embrace their inner rationality, leading them to the splendid result of \( \frac{2\sqrt{3}}{3} \)!