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Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $-\sqrt{-38}$

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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{-38}

Recognize imaginary unit involvement: First, recognize that the square root of a negative number involves the imaginary unit $i$ , where $i^2 = -1$ .
Write expression as product: Write $-\sqrt{-38}$ as $-\sqrt{-1 \times 38}$ .
Split square root: Split the square root into $-\sqrt{-1} \times \sqrt{38}$ .
Replace $\sqrt{-1}$ with $i$ : Replace $\sqrt{-1}$ with $i$ to get $-i \times \sqrt{38}$ .
Simplify expression: Simplify the expression to $-i \sqrt{38}$ .

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