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Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $-\sqrt{-49}$

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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{-49}

Express as product: First, let's express $-\sqrt{-49}$ as the product of square roots and $\sqrt{-1}$ . $\newline$ $-\sqrt{-49} = -\sqrt{-1 \times 49}$
Use $i$ for $\sqrt{-1}$ : Now, let's use $i$ to represent $\sqrt{-1}$ and simplify the square root of $49$ . $\newline$ $-\sqrt{-1 \times 49} = -i \times \sqrt{49}$
Simplify $\sqrt{49}$ : Simplify $\sqrt{49}$ to get $7$ .
$-i \times \sqrt{49} = -i \times 7$
Multiply to get complex number: Finally, multiply $-i$ by $7$ to get the complex number. $\newline$ $-i \times 7 = -7i$

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