To express \(-\sqrt{-40}\) as a complex number in the standard form \(a + bi\):
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First, we simplify \(-\sqrt{-40}\): \[ -\sqrt{-40} = -\sqrt{40} \cdot \sqrt{-1} \] Since \(\sqrt{-1} = i\), we can rewrite this as: \[ -\sqrt{40} \cdot i \]
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Next, we simplify \(\sqrt{40}\): \[ \sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \cdot \sqrt{10} = 2\sqrt{10} \]
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Now, substituting back into our expression, we have: \[ -\sqrt{-40} = -2\sqrt{10} \cdot i \] This can be written as: \[ 0 - 2\sqrt{10}i \]
Thus, in standard form \(a + bi\), we identify \(a = 0\) and \(b = -2\sqrt{10}\).
The correct answer is: \[ 0 - 2\sqrt{10}i \]
None of the provided options seem to directly match \(0 - 2\sqrt{10}i\). If the options are meant to be interpreted as: \[ -2\sqrt{10} i \] In the context of standard form, this is \(-2\sqrt{10}i\), which is equivalent to \(0 + (-2\sqrt{10})i\).
Please verify the options you provided, as the answer derived is a standard re-expression of \(-\sqrt{-40}\).