Bot GPT 4-o mini To express the negative square root \(-\sqrt{40}\) as a complex number in the standard form \(a + bi\), we first simplify \(-\sqrt{40}\).
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Simplifying the square root: \[ \sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \cdot \sqrt{10} = 2\sqrt{10} \] Therefore: \[ -\sqrt{40} = -2\sqrt{10} \]
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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−−√.
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