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Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $-\sqrt{-60}$

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Introduction to complex numbers

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Q. Use the imaginary number

i

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

-\sqrt{-60}

Express as product: First, let's express $-\sqrt{-60}$ as the product of square roots and $\sqrt{-1}$ . $\newline$ $-\sqrt{-60} = -\sqrt{-1 \times 60}$
Rewrite and simplify: Now, let's rewrite $-\sqrt{-1}$ as $i$ and $\sqrt{60}$ as $\sqrt{4\times15}$ to simplify the radical. $\newline$ $-\sqrt{-60} = -i \times \sqrt{4\times15}$
Simplify radical: We know that $\sqrt{4}$ is $2$ , so we can simplify further. $\newline$ $-i \cdot \sqrt{4\cdot15} = -i \cdot \sqrt{4} \cdot \sqrt{15}$
Do multiplication: Now, let's do the multiplication. $\newline$ $-i \times \sqrt{4} \times \sqrt{15} = -i \times 2 \times \sqrt{15}$
Final complex number: Finally, we multiply $-i$ by $2$ to get the simplified complex number. $-i \times 2 \times \sqrt{15} = -2i \times \sqrt{15}$

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