To express \(-6\sqrt{-20}\) as a complex number in the standard form \(a + bi\), we start by simplifying the expression step by step.
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Simplify \(-20\): \[ -20 = 20 \cdot -1 \]
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Take the square root of \(-20\): \[ \sqrt{-20} = \sqrt{20} \cdot \sqrt{-1} = \sqrt{20} \cdot i \] The square root of 20 can be simplified: \[ \sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5} \] Thus, \[ \sqrt{-20} = 2\sqrt{5}i \]
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Multiply by \(-6\): \[ -6\sqrt{-20} = -6 \cdot (2\sqrt{5}i) = -12\sqrt{5}i \]
Now, we see that \(-6\sqrt{-20}\) is re-expressed as: \[ -12\sqrt{5}i \]
This matches the option:
- -12√5i
Thus, the correct response is -12√5i.