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Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $\sqrt{-64}$

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Introduction to complex numbers

Full solution

Q. Use the imaginary number

i

to rewrite the expression below as a complex number. Simplify all radicals.

\sqrt{-64}

Recognize Imaginary Unit: First, recognize that the square root of a negative number involves the imaginary unit $i$ . $\sqrt{-64} = \sqrt{-1 \times 64}$
Separate $-1$ and $64$ : Next, separate the square root of $-1$ , which is $i$ , from the square root of $64$ . $\sqrt{-1 \times 64} = \sqrt{-1} \times \sqrt{64}$
Simplify Square Root: Now, simplify the square root of $64$ , which is $8$ . $\sqrt{64} = 8$
Combine with Imaginary Unit: Combine the imaginary unit $i$ with the simplified square root of $64$ . $\sqrt{-1} \times \sqrt{64} = i \times 8$
Write as Complex Number: Finally, write the expression as a complex number. $i \times 8 = 8i$

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