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Which expression represents the square root of -64 in terms of i?

8i

To find the square root of -64 in terms of the imaginary unit \( i \), we first recognize that the square root of a negative number can be expressed using \( i \), where \( i \) is defined as the square root of -1.

The expression \( \sqrt{-64} \) can be rewritten as:

\[

\sqrt{-64} = \sqrt{64} \times \sqrt{-1}

\]

Calculating \( \sqrt{64} \) gives us 8, while \( \sqrt{-1} \) corresponds to \( i \). Therefore, the expression simplifies to:

\[

\sqrt{-64} = 8 \times i = 8i

\]

This confirms that the correct representation of the square root of -64 in terms of \( i \) is \( 8i \). This choice accurately reflects the relationship between the square root of negative numbers and the imaginary unit. Other options do not apply because they either result in real numbers or do not account for the imaginary component correctly.

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