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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}

Identify Imaginary Unit: Now, we know that $\sqrt{-1}$ is the imaginary unit $i$ . So we can write $-\sqrt{-10}$ as $-i \times \sqrt{10}$ .
Convert to Complex Form: Finally, we simplify $\sqrt{10}$ to get the complex number in the form $a + bi$ . But wait, $\sqrt{10}$ is already in its simplest radical form, so we don't need to simplify further.

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