Question

Which of the following re-expresses the negative square root −40−−−−√ as a complex number in the standard form a+bi ?(1 point)
Responses

4i10−−√
4 i Start Root 10 End Root

2i10−−√
2 i Start Root 10 End Root

210i−−−√
2 Start Root 10 i End Root

210−−√

Answer 1

To express the negative square root \(-\sqrt{40}\) as a complex number in the standard form \(a + bi\), we first simplify \(-\sqrt{40}\).

1. **Simplifying the square root**:
\[
\sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \cdot \sqrt{10} = 2\sqrt{10}
\]
Therefore:
\[
-\sqrt{40} = -2\sqrt{10}
\]

2. **Expressing as a complex number**:
Since \(-2\sqrt{10}\) is a real number (and not a complex number), we can express it in the form \(a + bi\):
\[
-2\sqrt{10} + 0i
\]

However, if we are interpreting the problem to express the square root of \(-40\) (instead of \(-\sqrt{40}\)), then:
\[
\sqrt{-40} = \sqrt{40} \cdot i = 2\sqrt{10} i
\]

Putting it all together, the correct expression for \(-\sqrt{-40}\) would be:
- **For \(-\sqrt{40}\)**: \(-2\sqrt{10} + 0i\) (which isn't represented in your options).
- **For \(\sqrt{-40}\)**: \(2\sqrt{10} i\).

Among your options, the closest and correct response for \(\sqrt{-40} = 2 \sqrt{10} i\) would be:
\[
2i\sqrt{10}
\]

Thus, the correct answer is:
**2i10−−√**.