Question

Which of the following re-expresses the negative square root  −40−−−−√  as a complex number in the standard form  a+bi ?(1 point)Responses210−−√2 Start Root 10 End Root2i10−−√2 i Start Root 10 End Root4i10−−√4 i Start Root 10 End Root210i−−−√

Answer 1

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

1. We know that \(\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}\).
2. Therefore, \(-\sqrt{40} = -2\sqrt{10}\).

Since \(-2\sqrt{10}\) is a real number, we can express it as:

\[
-2\sqrt{10} + 0i
\]

This means \(a = -2\sqrt{10}\) and \(b = 0\).

In the provided response options, it appears that we might be looking for a complex number that represents this expression. However, none of the options you provided directly translate to \(-2\sqrt{10}\).

The correct expression you need in the standard form \(a + bi\) is:
\[
-2\sqrt{10} + 0i
\]

If we were to look at options that involve purely imaginary terms (with some confusion possibly), the correct form should ideally include \(-2\sqrt{10}\) without any associated imaginary unit unless stated, totaling to \(0i\).

Please clarify or check the options again, as none of them fit the simplified expression of \(-\sqrt{40}\) exactly as a complex number.