Question
The Existence of Imaginary Numbers Quick Check
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–√
Answers
GPT-4o mini
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.)
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.)