To re-express \(-\sqrt{40}\) as a complex number in the standard form \(a+bi\):
- First, note that \(-\sqrt{40}\) can be rewritten as \(-\sqrt{4 \times 10} = -\sqrt{4} \sqrt{10} = -2\sqrt{10}\).
- Since the expression is negative, we can express it as \(0 - 2\sqrt{10}\), which can be transformed into a complex number by recognizing that \(-2\sqrt{10}\) can be expressed with an imaginary unit \(i\): \(-2\sqrt{10} = 0 + (-2\sqrt{10})i\).
Thus, the standard form \(a + bi\) here is \(0 - 2\sqrt{10}i\).
Now let's match this with the provided options:
- 2i√10
- 2√10i
- 4i√10
- 2√10
None of the given options directly match the negative value we obtained, but looking at \(2i\sqrt{10}\) and \(2\sqrt{10}i\), we see that the second option matches in terms of structure, but not in sign.
The correct way to express \(-\sqrt{40}\) in standard form is indeed in the form of \( -2\sqrt{10}i\), which is not one of the responses listed.
If we consider the standard forms provided, the closest one consistent with the approach would be \(2\sqrt{10}i\) assuming we're targeting the inequality of the imaginary number because of opposite signs (indicating the direction on the imaginary line).
In conclusion, if we follow the convention of always taking one correct standard form, the closest answer which utilizes \(i\) is \(2\sqrt{10}i\) if we're looking at magnitude irrespective of its sign.
However, it must be noted that none of the provided options reflect the required negativity clearly, which creates ambiguity in choosing a correct response.
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