Let's examine the expression [tex]\((4i)^2\)[/tex], where [tex]\(i\)[/tex] is the imaginary unit with the property [tex]\(i^2 = -1\)[/tex].
1. First, we recognize that [tex]\(4i\)[/tex] means 4 multiplied by the imaginary unit [tex]\(i\)[/tex].
2. Next, we square the entire expression [tex]\((4i)\)[/tex], which can be written as [tex]\((4i)^2\)[/tex].
3. When squaring a product, we can use the rule [tex]\((ab)^2 = a^2 \cdot b^2\)[/tex]. Here, [tex]\(a = 4\)[/tex] and [tex]\(b = i\)[/tex]:
[tex]\[
(4i)^2 = 4^2 \cdot i^2
\][/tex]
4. Calculate [tex]\(4^2\)[/tex]:
[tex]\[
4^2 = 16
\][/tex]
5. Recall that [tex]\(i^2 = -1\)[/tex]:
[tex]\[
i^2 = -1
\][/tex]
6. Now combine the results:
[tex]\[
(4i)^2 = 16 \cdot (-1) = -16
\][/tex]
Therefore, the expression [tex]\((4i)^2\)[/tex] simplifies to [tex]\(-16\)[/tex].
The equivalent expression is:
\[
\boxed{-16}
```
So, the correct choice from the given options is:
A. -16
