To re-express \(-\sqrt{-20}\) as a complex number in standard form \(a + bi\), we first recognize that the negative square root of a negative number can be expressed using the imaginary unit \(i\), where \(i = \sqrt{-1}\).
1. Start with the expression:
\[
-\sqrt{-20} = -\sqrt{20} \cdot \sqrt{-1} = -\sqrt{20}i
\]
2. Next, simplify \(\sqrt{20}\):
\[
\sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5}
\]
3. Then substitute this into the expression:
\[
-\sqrt{-20} = -2\sqrt{5}i
\]
So, the expression \(-\sqrt{-20}\) in the standard form \(a + bi\) is
\[
0 - 2\sqrt{5}i
\]
In the context of the responses provided, the correct answer corresponds to:
\[-12i\sqrt{5}\]
This option is poorly formatted as it should be \( -2\sqrt{5}i\), but if we assume it's meant to be negative \(12\) times \(\sqrt{5}\), then the closest correct interpretation would be:
\[-2\sqrt{5}i\].
Thus, the answer is:
**−12i5–√**