Question

Express $\left(-\sqrt{3}+\sqrt{-2}\right)\left(2\sqrt{3}-i\right)$ in the form $a + ib$.

• A. $\left(1-2\sqrt{2}\right)i$
• B. $\left(1+2\sqrt{2}\right)i$
• C. $\left(-6-\sqrt{2}\right)+\sqrt{3}\left(1+2\sqrt{2}\right)i$
• D. $\left(-6+\sqrt{2}\right)+\sqrt{3}\left(1+2\sqrt{2}\right)i$

Answer 1

Answer: (D)

$\left(-\sqrt{3}+\sqrt{-2}\right)\left(2\sqrt{3}-i\right)$
$=\left(-\sqrt{3}+\sqrt{2}i\right)\left(2\sqrt{3}-i\right)$
$=-6+\sqrt{3}i+2\sqrt{6}i-\sqrt{2}i^{2}$
$=\left(-6+\sqrt{2}\right)+\sqrt{3}\left(1+2\sqrt{2}\right)i$