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Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $\sqrt{-10}$

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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{-10}

Recognize Imaginary Unit $i$ : First, recognize that the square root of a negative number involves the imaginary unit $i$ , where $i$ is defined as the square root of $-1$ .
Express as Product: Express $\sqrt{-10}$ as $\sqrt{-1 \times 10}$ .
Separate Square Roots: Now, separate the square roots to get $\sqrt{-1} \times \sqrt{10}$ .
Replace with i: Replace $\sqrt{-1}$ with $i$ to get $i \times \sqrt{10}$ .
Final Simplified Form: Since there's no simplification needed for $\sqrt{10}$ , the expression is already in its simplest form.

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