Which of the following re-expresses the negative square root −6−20−−−−√ as a complex number in the standard form a+bi?(1 point)

Question

Responses

2i5–√
2 i Start Root 5 End Root

−125–√
negative 12 Start Root 5 End Root

−125i−−√
negative 12 Start Root 5 i End Root

−12i5–√

Answer 1

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–√