The Existence of Imaginary Numbers Quick Check

Question

4 of 54 of 5 Items
Question
Which of the following re-expresses the negative square root −6−20−−−−√ as a complex number in the standard form a+bi ?(1 point)
Responses

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

−125–√
negative 12 Start Root 5 End Root

2i5–√
2 i Start Root 5 End Root

−12i5–√

Answer 1

To express the negative square root \(-\sqrt{-20}\) as a complex number in standard form \(a + bi\), we first recognize that we can factor out the negative sign to use the property of imaginary numbers.

The calculation would look like this:

\[ -\sqrt{-20} = -\sqrt{20} \cdot i = -\sqrt{4 \cdot 5} \cdot i = -2\sqrt{5} \cdot i \]

So, in standard form \(a + bi\), we have:

\[ 0 - 2\sqrt{5}i \]

Thus, it would be expressed as:

\(-2\sqrt{5}i\)

The correct response from the options provided is:

−12i5–√ (−2√5 i).

(Note: Make sure to write it correctly as shown since the formatting might vary slightly.)