To re-express the negative square root \( -\sqrt{6 - 20} \) as a complex number in the standard form \( a + bi \), let's first simplify the expression inside the square root.
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Calculate \( 6 - 20 \): \[ 6 - 20 = -14 \]
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Rewrite the expression: \[ -\sqrt{-14} \]
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We can express the square root of a negative number using the imaginary unit \( i \): \[ -\sqrt{-14} = -\sqrt{14} \cdot i \]
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Therefore, the expression becomes: \[ -\sqrt{14} \cdot i \]
Now, among the provided options, we need to check which corresponds to this result. The potential answers, however, seem to not directly reflect our simplified form, which could likely stem from a typographical or interpretation error.
The closest form we can deduce related to \( \sqrt{14} \) does not appear in the options given. If you want it in terms of specific options given, then the closest distinctively written form \( a + bi \) would be \( 0 - \sqrt{14} i \), but it looks like there's a disparity with the listed options and could require alerting the source of the question.
Nonetheless, if we were allowed to interpret \( \sqrt{14} \) in a factorized form of \( 14 = 2 \cdot 7 \), we would have \( -\sqrt{2 \cdot 7} \cdot i = - \sqrt{2} \sqrt{7} \cdot i \) but again, this would still not align you with any given answer without clear referencing from your question.
In evaluating the answer choices provided:
- They require a relation with \( \sqrt{5} \). Hence clarifying your condition on \( 14 \) with respect to \( 5 \) could possibly offer insight into concluding which specifically matches, but abide by searching distinctly.
Consequently, there might be an error in the original options provided. Please consider verifying or re-expressing the options appropriately.
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