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Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $-\sqrt{-4}$

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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{-4}

Breakdown into parts: First, let's break $-\sqrt{-4}$ into $-1 \times \sqrt{-1 \times 4}$ .
Use of imaginary unit: Now, we know that $\sqrt{-1}$ is the imaginary unit $i$ , so we can rewrite the expression as $-1 \times i \times \sqrt{4}$ .
Simplify square root: Simplifying $\sqrt{4}$ gives us $2$ , so the expression becomes $-1 \times i \times 2$ .
Final expression: Multiplying $-1 \times 2$ gives $-2$ , so the final expression is $-2i$ .

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