To express \(\sqrt{-40}\) as a complex number in the standard form \(a + bi\), we can follow these steps:
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Recognize that \(\sqrt{-40}\) can be rewritten using the property of square roots: \[ \sqrt{-40} = \sqrt{40} \cdot \sqrt{-1} = \sqrt{40} \cdot i \]
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Now, calculate \(\sqrt{40}\): \[ \sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \cdot \sqrt{10} = 2\sqrt{10} \]
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Therefore, we can express \(\sqrt{-40}\) as: \[ \sqrt{-40} = 2\sqrt{10} \cdot i = 0 + 2\sqrt{10}i \]
This matches the form \(a + bi\) with \(a = 0\) and \(b = 2\sqrt{10}\).
Thus, the re-expressed form of \(\sqrt{-40}\) is: \[ \boxed{2i \sqrt{10}} \]
This corresponds to the option 2i * sqrt(10).