Simplify. Express in terms of $$ i $$. $$ (\sqrt{-11})(\sqrt{-3}) $$

Question

UpStudy AI · Accepted Answer

We start by rewriting each square root with a negative radicand in terms of $$ i $$:

$$
\sqrt{-11} = i\sqrt{11} \quad \text{and} \quad \sqrt{-3} = i\sqrt{3}
$$

Next, multiply these two expressions:

$$
(\sqrt{-11})(\sqrt{-3}) = (i\sqrt{11})(i\sqrt{3}) = i^2 (\sqrt{11}\sqrt{3})
$$

Since $$ i^2 = -1 $$ and $$\sqrt{11}\sqrt{3} = \sqrt{33}$$, we have:

$$
(\sqrt{-11})(\sqrt{-3}) = -\sqrt{33}
$$

Thus, the simplified form in terms of $$ i $$ is:

$$
-\sqrt{33}
$$
$$ -\sqrt{33} $$

Simplify. Express in terms of .