To solve for the value of [tex]\(\sqrt{-9} \times \sqrt{-16}\)[/tex], we need to work with the properties of complex numbers and imaginary units.
1. First, recognize that the square root of a negative number involves the imaginary unit [tex]\(i\)[/tex], where [tex]\(i = \sqrt{-1}\)[/tex].
2. Calculate [tex]\(\sqrt{-9}\)[/tex]:
[tex]\[
\sqrt{-9} = \sqrt{9 \times -1} = \sqrt{9} \times \sqrt{-1} = 3i
\][/tex]
3. Similarly, calculate [tex]\(\sqrt{-16}\)[/tex]:
[tex]\[
\sqrt{-16} = \sqrt{16 \times -1} = \sqrt{16} \times \sqrt{-1} = 4i
\][/tex]
4. Now, multiply the two results:
[tex]\[
\sqrt{-9} \times \sqrt{-16} = (3i) \times (4i)
\][/tex]
5. Use the property of multiplication for imaginary numbers [tex]\(i \times i = i^2\)[/tex]:
[tex]\[
(3i) \times (4i) = 3 \times 4 \times i^2 = 12 \times i^2
\][/tex]
6. Recall that [tex]\(i^2 = -1\)[/tex]:
[tex]\[
12 \times i^2 = 12 \times (-1) = -12
\][/tex]
Therefore, the value of [tex]\(\sqrt{-9} \times \sqrt{-16}\)[/tex] is [tex]\(-12\)[/tex].
Thus, the correct answer is:
B. -12
